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Volumn 4, Issue 4, 1998, Pages 735-764

Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth

Author keywords

Asynchronous exponential growth; Cumulative outputs; Eventual and essential compactness; Growth bounds; Integrated semigroups; Positive perturbation; Resolvent outputs; Resolvent positive operator; Semigroups; Spectral bound; Stieltjes integral equations

Indexed keywords


EID: 0032365243     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1998.4.735     Document Type: Article
Times cited : (55)

References (68)
  • 1
    • 84972536242 scopus 로고
    • Evolution operators and strong solutions of abstract linear parabolic equations
    • Acquistapace, P. (1988): Evolution operators and strong solutions of abstract linear parabolic equations. Diff. Int. Eq. 4, 433-457
    • (1988) Diff. Int. Eq. , vol.4 , pp. 433-457
    • Acquistapace, P.1
  • 2
    • 51649147034 scopus 로고
    • Vector-valued Laplace transforms and Cauchy problems
    • Arendt, W. (1987a): Vector-valued Laplace transforms and Cauchy problems. Israel J. Math. 59, 327-351
    • (1987) Israel J. Math. , vol.59 , pp. 327-351
    • Arendt, W.1
  • 3
    • 84960611544 scopus 로고
    • Resolvent positive operators
    • Arendt, W. (1987b): Resolvent positive operators. Proc. London Math. Soc. 54, 321-349
    • (1987) Proc. London Math. Soc. , vol.54 , pp. 321-349
    • Arendt, W.1
  • 4
    • 3042969787 scopus 로고
    • Vector-valued versions of some representation theorems in real analysis
    • Functional Analysis (K.D. Bierstedt, A. Pietsch, W.M. Ruess, D. Vogt; eds.), Marcel Dekker
    • Arendt, W. (1994a): Vector-valued versions of some representation theorems in real analysis. Functional Analysis (K.D. Bierstedt, A. Pietsch, W.M. Ruess, D. Vogt; eds.), 33-50. Lecture Notes in Pure and Applied Mathematics 150. Marcel Dekker
    • (1994) Lecture Notes in Pure and Applied Mathematics , vol.150 , pp. 33-50
    • Arendt, W.1
  • 5
    • 0041835763 scopus 로고
    • Inegalités de Kato et semi-groupes sous-Markoviens
    • Arendt, W.; Bénilan, Ph. (1992): Inegalités de Kato et semi-groupes sous-Markoviens. Revista Matematica, 5, 279-308
    • (1992) Revista Matematica , vol.5 , pp. 279-308
    • Arendt, W.1    Bénilan, Ph.2
  • 6
    • 0040270169 scopus 로고
    • Generation of linear semigroups
    • (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), North Holland
    • Clément, Ph. (1987): Generation of linear semigroups. One-Parameter Semigroups (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), 47-92. North Holland
    • (1987) One-Parameter Semigroups , pp. 47-92
    • Clément, Ph.1
  • 8
    • 0001423998 scopus 로고
    • Irreducible compact operators
    • de Pagter, B. (1986): Irreducible compact operators. Math. Z. 192, 149-153
    • (1986) Math. Z. , vol.192 , pp. 149-153
    • De Pagter, B.1
  • 10
    • 84972525241 scopus 로고
    • Perturbing semigroups by solving Stieltjes renewal equations
    • Diekmann, O.; Gyllenberg, M.; Thieme, H.R. (1993): Perturbing semigroups by solving Stieltjes renewal equations. Diff. Int. Eq. 6, 155-181
    • (1993) Diff. Int. Eq. , vol.6 , pp. 155-181
    • Diekmann, O.1    Gyllenberg, M.2    Thieme, H.R.3
  • 11
    • 84972545683 scopus 로고
    • Perturbing evolutionary systems by step responses and cumulative outputs
    • Diekmann, O.; Gyllenberg, M.; Thieme, H.R. (1995): Perturbing evolutionary systems by step responses and cumulative outputs. Diff. Int. Eq. 8, 1205-1244
    • (1995) Diff. Int. Eq. , vol.8 , pp. 1205-1244
    • Diekmann, O.1    Gyllenberg, M.2    Thieme, H.R.3
  • 12
    • 0010460955 scopus 로고
    • The 'cumulative' formulation of (physiologically) structured population models
    • Evolution Equations, Control Theory, and Biomathematics (Ph. Clément, G. Lumer; eds), Marcel Dekker
    • Diekmann, O.; Gyllenberg, M.; Metz, J.A.J.; Thieme, H.R. (1994): The 'cumulative' formulation of (physiologically) structured population models. Evolution Equations, Control Theory, and Biomathematics (Ph. Clément, G. Lumer; eds), 145-154. Lecture Notes in Pure and Applied Mathematics 155, Marcel Dekker
    • (1994) Lecture Notes in Pure and Applied Mathematics , vol.155 , pp. 145-154
    • Diekmann, O.1    Gyllenberg, M.2    Metz, J.A.J.3    Thieme, H.R.4
  • 14
    • 0000201875 scopus 로고    scopus 로고
    • On the formulation and analysis of general deterministic structured population models. I. Linear Theory
    • Diekmann, O.; Gyllenberg, M.; Metz, J.A.J.; Thieme, H.R. (1998): On the formulation and analysis of general deterministic structured population models. I. Linear Theory. J. Math. Biol., 349-388.
    • (1998) J. Math. Biol. , pp. 349-388
    • Diekmann, O.1    Gyllenberg, M.2    Metz, J.A.J.3    Thieme, H.R.4
  • 16
    • 0001461464 scopus 로고
    • Time dependent perturbations and scattering of strongly continuous groups on Banach spaces
    • Evans, D.A. (1976): Time dependent perturbations and scattering of strongly continuous groups on Banach spaces. Math. Annal. 221, 275-290
    • (1976) Math. Annal. , vol.221 , pp. 275-290
    • Evans, D.A.1
  • 18
    • 0040845687 scopus 로고
    • Green Functions for Second Order Parabolic Integro-Differential Problems
    • Longman
    • Garroni, M.G.; Menaldi, J.L. (1992): Green Functions for Second Order Parabolic Integro-Differential Problems. Pitman Research Notes in Mathematics 275. Longman
    • (1992) Pitman Research Notes in Mathematics , vol.275
    • Garroni, M.G.1    Menaldi, J.L.2
  • 19
    • 3042889486 scopus 로고
    • Order structure of the semigroup dual: A counterexample
    • Grabosch, A.; Nagel, R.: (1989): Order structure of the semigroup dual: a counterexample. Indag. Math. 92, 199-201
    • (1989) Indag. Math. , vol.92 , pp. 199-201
    • Grabosch, A.1    Nagel, R.2
  • 20
    • 0000695762 scopus 로고
    • 0(X)
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • 0(X). One-parameter Semigroups of Positive operators (R. Nagel, ed.), 163-203. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 163-203
    • Greiner, G.1
  • 21
    • 0013407747 scopus 로고
    • Compact and quasi-compact semigroups
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Greiner, G. (1986b): Compact and quasi-compact semigroups. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 209-218. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 209-218
    • Greiner, G.1
  • 22
    • 0000695762 scopus 로고
    • Spectral theory of positive semigroups on Banach lattices
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Greiner, G. (1986c): Spectral theory of positive semigroups on Banach lattices. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 292-332. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 292-332
    • Greiner, G.1
  • 23
    • 0000695762 scopus 로고
    • Spectral theory of semigroups on Banach Spaces
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Greiner, G.; Nagel, R. (1986a): Spectral theory of semigroups on Banach Spaces. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 60-97. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 60-97
    • Greiner, G.1    Nagel, R.2
  • 24
    • 3042927866 scopus 로고
    • Convergence of positive semigroups
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Greiner, G.; Nagel, R. (1986b): Convergence of positive semigroups. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 342-355. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 342-355
    • Greiner, G.1    Nagel, R.2
  • 25
    • 0000695762 scopus 로고
    • Stability of positive semigroups on Banach lattices
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Greiner, G.; Neubrander, F. (1986): Stability of positive semigroups on Banach lattices. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 334-342. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 334-342
    • Greiner, G.1    Neubrander, F.2
  • 26
    • 0000764850 scopus 로고
    • On the spectral bound of the generator of semigroups of positive operators
    • Greiner, G; Voigt, J.; Wolff, M. (1981): On the spectral bound of the generator of semigroups of positive operators. J. Operator Th. 5, 245-256
    • (1981) J. Operator Th. , vol.5 , pp. 245-256
    • Greiner, G.1    Voigt, J.2    Wolff, M.3
  • 27
    • 0022553346 scopus 로고
    • The size and scar distribution of the yeast Saccharomyces cerevisiae
    • Gyllenberg, M. (1986): The size and scar distribution of the yeast Saccharomyces cerevisiae. J. Math. Biol. 24, 81-101
    • (1986) J. Math. Biol. , vol.24 , pp. 81-101
    • Gyllenberg, M.1
  • 28
    • 0006699470 scopus 로고
    • Perron-Frobenius theory for positive semigroups
    • (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), North Holland
    • Heijmans, H.J.A.M. (1987a): Perron-Frobenius theory for positive semigroups. One-Parameter Semigroups (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), 193-211. North Holland
    • (1987) One-Parameter Semigroups , pp. 193-211
    • Heijmans, H.J.A.M.1
  • 29
    • 0040864460 scopus 로고
    • Two examples from structured population dynamics
    • (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), North Holland
    • Heijmans, H.J.A.M. (1987b): Two examples from structured population dynamics. One-Parameter Semigroups (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), 235-244 North Holland
    • (1987) One-Parameter Semigroups , pp. 235-244
    • Heijmans, H.J.A.M.1
  • 30
    • 0040864462 scopus 로고
    • Asymptotic behavior
    • (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), North Holland
    • Heijmans, H.J.A.M.; de Pagter, B. (1987): Asymptotic behavior. One-Parameter Semigroups (Clément, Ph.; Heijmans, H.J.A.M.; Angenent, S.; van Duijn, C.J.; de Pagter, B.; eds.), 213-233. North Holland
    • (1987) One-Parameter Semigroups , pp. 213-233
    • Heijmans, H.J.A.M.1    De Pagter, B.2
  • 33
    • 0347723684 scopus 로고
    • Stationary scattering theory for time-dependent hamiltonians
    • Howland, J.S. (1974): Stationary scattering theory for time-dependent hamiltonians. Math. Annal. 207, 315-335
    • (1974) Math. Annal. , vol.207 , pp. 315-335
    • Howland, J.S.1
  • 34
    • 51249167814 scopus 로고
    • Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion
    • Huyer, W. (1994): Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion. Semigroup Forum 49, 99-114
    • (1994) Semigroup Forum , vol.49 , pp. 99-114
    • Huyer, W.1
  • 35
    • 85034486978 scopus 로고    scopus 로고
    • in the same Proceedings as in [63]
    • 2, in the same Proceedings as in [63], 713-732.
    • (1997) 2 , pp. 713-732
    • Huyer, W.1
  • 37
    • 0001622782 scopus 로고
    • Superconvexity of the spectral radius, and convexity of the spectral bound and the type
    • Kato, T. (1982): Superconvexity of the spectral radius, and convexity of the spectral bound and the type. Math. Z. 180, 265-273
    • (1982) Math. Z. , vol.180 , pp. 265-273
    • Kato, T.1
  • 39
    • 0021283893 scopus 로고
    • On the dynamics of chemically stressed populations: The deduction of population consequences from effects on the individuals
    • Kooijman, S.A.L.M.; Metz, J.A.J. (1984): On the dynamics of chemically stressed populations: The deduction of population consequences from effects on the individuals. Ecotox. 8, 254-274
    • (1984) Ecotox. , vol.8 , pp. 254-274
    • Kooijman, S.A.L.M.1    Metz, J.A.J.2
  • 43
    • 0001468782 scopus 로고
    • Evolutionary semigroups and Lyapunov theorems for Banach spaces
    • Latushkin, Y.; Montgomery-Smith, S. (1995): Evolutionary semigroups and Lyapunov theorems for Banach spaces. J. Funct. Anal. 127, 173-197
    • (1995) J. Funct. Anal. , vol.127 , pp. 173-197
    • Latushkin, Y.1    Montgomery-Smith, S.2
  • 44
    • 0003157238 scopus 로고
    • The Dynamics of Physiologically Structured Populations
    • Springer
    • Metz, J.A.J.; Diekmann, O. (1986): The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68. Springer
    • (1986) Lecture Notes in Biomathematics , vol.68
    • Metz, J.A.J.1    Diekmann, O.2
  • 45
    • 0003207468 scopus 로고
    • One-parameter Semigroups of Positive operators
    • Springer
    • Nagel, R. (ed., 1986): One-parameter Semigroups of Positive operators. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184
    • Nagel, R.1
  • 46
    • 0040864461 scopus 로고
    • Asymptotics of semigroups on Danach spaces
    • One-parameter Semigroups of Positive operators (R. Nagel, ed.), Springer
    • Neubrander, F. (1986): Asymptotics of semigroups on Danach spaces. One-parameter Semigroups of Positive operators (R. Nagel, ed.), 98-116. Lecture Notes in Mathematics 1184, Springer
    • (1986) Lecture Notes in Mathematics , vol.1184 , pp. 98-116
    • Neubrander, F.1
  • 47
    • 84972562394 scopus 로고
    • Integrated semigroups and their applications to the abstract Cauchy problem
    • Neubrander, F. (1988): Integrated semigroups and their applications to the abstract Cauchy problem. Pac. J. Math. 135, 111-155
    • (1988) Pac. J. Math. , vol.135 , pp. 111-155
    • Neubrander, F.1
  • 48
    • 27144435704 scopus 로고    scopus 로고
    • On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators
    • to appear
    • Nickel, G.; Rhandi, A. (to appear): On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators. Differential Integral Equations
    • Differential Integral Equations
    • Nickel, G.1    Rhandi, A.2
  • 49
    • 0000984231 scopus 로고
    • Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem
    • Fixed Point Theory (E. Fadell, G. Fournier; eds.), Springer
    • Nussbaum, R.D. (1981): Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem. Fixed Point Theory (E. Fadell, G. Fournier; eds.), 309-331. Lecture Notes in Mathematics 886. Springer
    • (1981) Lecture Notes in Mathematics , vol.886 , pp. 309-331
    • Nussbaum, R.D.1
  • 51
    • 0030097999 scopus 로고    scopus 로고
    • Perturbation and an abstract characterization of evolution semigroups
    • Räbiger, F.; Rhandi, A.; Schnaubelt, R. (1996): Perturbation and an abstract characterization of evolution semigroups. JMAA 189, 516-533
    • (1996) JMAA , vol.189 , pp. 516-533
    • Räbiger, F.1    Rhandi, A.2    Schnaubelt, R.3
  • 52
    • 0001069380 scopus 로고    scopus 로고
    • The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions
    • Räbiger, F.; Schnaubelt, R. (1996): The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions. Semigroup Forum 52, 225-240
    • (1996) Semigroup Forum , vol.52 , pp. 225-240
    • Räbiger, F.1    Schnaubelt, R.2
  • 53
    • 0000016443 scopus 로고
    • A spectral characterization of exponentially dichotomic and hyperbolic evolution families
    • preprint
    • Räbiger, F.; Schnaubelt, R. (preprint): A spectral characterization of exponentially dichotomic and hyperbolic evolution families. Tübinger Berichte zur Funktionalanalysis 3 (1993/94), 222-234
    • (1993) Tübinger Berichte Zur Funktionalanalysis , vol.3 , pp. 222-234
    • Räbiger, F.1    Schnaubelt, R.2
  • 54
    • 51249164392 scopus 로고
    • Hyperbolic evolution semigroups on vector valued functions
    • Rau, R. (1994a): Hyperbolic evolution semigroups on vector valued functions. Semigroup Forum 48, 107-118
    • (1994) Semigroup Forum , vol.48 , pp. 107-118
    • Rau, R.1
  • 55
    • 0001101604 scopus 로고
    • Hyperbolic evolution groups and dichotomic evolution families
    • Rau, R. (1994b): Hyperbolic evolution groups and dichotomic evolution families. J. Dyn. Diff. Eqs. 6, 335-350
    • (1994) J. Dyn. Diff. Eqs. , vol.6 , pp. 335-350
    • Rau, R.1
  • 58
    • 78650972825 scopus 로고
    • On the Hille-Yosida operators
    • Evolution Equations, Control Theory, and Biomathematics (Ph. Clément, G. Lumer, eds.), Marcel Dekker
    • Sinestrari, E. (1994): On the Hille-Yosida operators. Evolution Equations, Control Theory, and Biomathematics (Ph. Clément, G. Lumer, eds.), 537-543. Lecture Notes in Pure and Applied Mathematics 155. Marcel Dekker
    • (1994) Lecture Notes in Pure and Applied Mathematics , vol.155 , pp. 537-543
    • Sinestrari, E.1
  • 59
    • 38249016253 scopus 로고
    • Integrated semigroups and integrated solutions to abstract Cauchy problems
    • Thieme, H.R. (1990): Integrated semigroups and integrated solutions to abstract Cauchy problems. JMAA 152, 416-447
    • (1990) JMAA , vol.152 , pp. 416-447
    • Thieme, H.R.1
  • 60
    • 0004461919 scopus 로고
    • Analysis of age-structured population models with an additional structure
    • (O. Arino, D.E. Axelrod, M. Kimmel; eds.), Marcel Dekker
    • Thieme, H.R. (1991): Analysis of age-structured population models with an additional structure. Mathematical Population Dynamics (O. Arino, D.E. Axelrod, M. Kimmel; eds.), 115-126. Marcel Dekker
    • (1991) Mathematical Population Dynamics , pp. 115-126
    • Thieme, H.R.1
  • 62
    • 0032352740 scopus 로고    scopus 로고
    • Remarks on resolvent positive operators and their perturbation
    • Thieme, H.R. (1998): Remarks on resolvent positive operators and their perturbation. Disc. Cont. Dyn. Sys. 4, 73-90
    • (1998) Disc. Cont. Dyn. Sys. , vol.4 , pp. 73-90
    • Thieme, H.R.1
  • 63
    • 1642286688 scopus 로고    scopus 로고
    • Quasicompact semigroups via compact perturbations
    • (O. Arino, D. Axelrod, M. Kimmel; eds.), World Scientific
    • Thieme, H.R. (1997): Quasicompact semigroups via compact perturbations. Advances in Mathematical Population Dynamics: Molecules, Cells and Man (O. Arino, D. Axelrod, M. Kimmel; eds.), World Scientific, 691-711.
    • (1997) Advances in Mathematical Population Dynamics: Molecules, Cells and Man , pp. 691-711
    • Thieme, H.R.1
  • 64
    • 0003211003 scopus 로고
    • The Adjoint of a Semigroup of Linear Operators
    • Springer
    • van Neerven, J.M.A.M. (1992): The Adjoint of a Semigroup of Linear Operators. Lecture Notes in Mathematics 1529, Springer
    • (1992) Lecture Notes in Mathematics , vol.1529
    • Neerven, J.M.A.M.1
  • 66
    • 51249172768 scopus 로고
    • On resolvent positive operators and positive co-semigroups on AL-space
    • Voigt, J. (1989): On resolvent positive operators and positive co-semigroups on AL-space. Semigroup Forum 38, 263-266
    • (1989) Semigroup Forum , vol.38 , pp. 263-266
    • Voigt, J.1
  • 67
    • 84966207881 scopus 로고
    • An operator-theoretic formulation of asynchronous exponential growth
    • Webb, G.F. (1987): An operator-theoretic formulation of asynchronous exponential growth. Trans. AMS 303, 751-763
    • (1987) Trans. AMS , vol.303 , pp. 751-763
    • Webb, G.F.1
  • 68
    • 21844514432 scopus 로고
    • p spaces
    • p spaces. Proc. AMS 123, 3089-3094
    • (1995) Proc. AMS , vol.123 , pp. 3089-3094
    • Weis, L.1


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