메뉴 건너뛰기




Volumn 8, Issue 3, 2002, Pages 519-562

Eigenvalues for a class of homogeneous cone maps arising from max-plus operators

Author keywords

Cone; Max plus operator; Measure of noncompactness; Nonlinear eigenvalue problem; Spectral radius

Indexed keywords


EID: 0036014244     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.519     Document Type: Article
Times cited : (78)

References (42)
  • 4
    • 0002154729 scopus 로고
    • Linear operators in complete positive cones
    • F.F. Bonsall, Linear operators in complete positive cones, Proc. London Math. Soc. (3) 8 (1958), pp. 53-75.
    • (1958) Proc. London Math. Soc. , vol.8 , Issue.3 , pp. 53-75
    • Bonsall, F.F.1
  • 5
    • 84972517829 scopus 로고
    • A further generalization of the Schauder fixed point theorem
    • F.E. Browder, A further generalization of the Schauder fixed point theorem, Duke Math. J. 32 (1965), pp. 575-578.
    • (1965) Duke Math. J. , vol.32 , pp. 575-578
    • Browder, F.E.1
  • 6
    • 0011517951 scopus 로고
    • Asymptotic fixed point theorems
    • F.E. Browder, Asymptotic fixed point theorems, Math. Ann. 185 (1970), pp. 38-60.
    • (1970) Math. Ann. , vol.185 , pp. 38-60
    • Browder, F.E.1
  • 7
    • 0001546913 scopus 로고
    • An additive eigenvalue problem of physics related to linear programming
    • W. Chou and R.J. Duffin, An additive eigenvalue problem of physics related to linear programming, Adv. Appl. Math. 8 (1987), pp. 486-498.
    • (1987) Adv. Appl. Math. , vol.8 , pp. 486-498
    • Chou, W.1    Duffin, R.J.2
  • 8
    • 25744452815 scopus 로고
    • Ground states of one-dimensional systems using effective potentials
    • W. Chou and R.B. Griffiths, Ground states of one-dimensional systems using effective potentials, Phys. Rev. B 34 (1986), pp. 6219-6234.
    • (1986) Phys. Rev. B , vol.34 , pp. 6219-6234
    • Chou, W.1    Griffiths, R.B.2
  • 10
    • 0002965087 scopus 로고
    • Punti uniti in trasformazioni a condiminio non compatto
    • G. Darbo, Punti uniti in trasformazioni a condiminio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), pp. 84-92.
    • (1955) Rend. Sem. Mat. Univ. Padova , vol.24 , pp. 84-92
    • Darbo, G.1
  • 14
    • 0031233725 scopus 로고    scopus 로고
    • Risk-sensitive control of finite state machines on an infinite horizon I
    • W.H. Fleming and D. Hernández-Hernández, Risk-sensitive control of finite state machines on an infinite horizon I, SIAM J. Control Optim. 35 (1997), pp. 1790-1810.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1790-1810
    • Fleming, W.H.1    Hernández-Hernández, D.2
  • 15
    • 0344240115 scopus 로고    scopus 로고
    • Risk-sensitive control of finite state machines on an infinite horizon II
    • W.H. Fleming and D. Hernández-Hernández, Risk-sensitive control of finite state machines on an infinite horizon II, SIAM J. Control Optim. 37 (1999), pp. 1048-1069.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1048-1069
    • Fleming, W.H.1    Hernández-Hernández, D.2
  • 16
    • 0000873359 scopus 로고    scopus 로고
    • A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering
    • W.H. Fleming and W.M. McEneaney, A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering, SIAM J. Control Optim. 38 (2000), pp. 683-710.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 683-710
    • Fleming, W.H.1    McEneaney, W.M.2
  • 17
    • 0011466835 scopus 로고
    • Numerical procedure for solving a minimization eigenvalue problem
    • L.M. Floría and R.B. Griffiths, Numerical procedure for solving a minimization eigenvalue problem, Numerische Math. 55 (1989), pp. 565-574.
    • (1989) Numerische Math. , vol.55 , pp. 565-574
    • Floría, L.M.1    Griffiths, R.B.2
  • 18
    • 0002451501 scopus 로고
    • Frenkel-Kontorova models of commensurate-incommensurate phase transitions
    • H. van Beijeren, editor, North-Holland, Amsterdam
    • R.B. Griffiths, Frenkel-Kontorova models of commensurate-incommensurate phase transitions, in: Fundamental Problems in Statistical Mechanics VII (Altenberg, 1989), H. van Beijeren, editor, North-Holland, Amsterdam, 1990, pp. 69-110.
    • (1990) Fundamental Problems in Statistical Mechanics VII (Altenberg, 1989) , pp. 69-110
    • Griffiths, R.B.1
  • 19
    • 0344233419 scopus 로고    scopus 로고
    • Idempotency (Bristol, 1994)
    • Cambridge Univ. Press, Cambridge
    • J. Gunawardena, editor, Idempotency (Bristol, 1994), Publications of the Newton Institute 11, Cambridge Univ. Press, Cambridge, 1998.
    • (1998) Publications of the Newton Institute , vol.11
    • Gunawardena, J.1
  • 20
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • American Mathematical Society, Providence
    • J.K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs 25, American Mathematical Society, Providence, 1988.
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 21
    • 0001391363 scopus 로고
    • A characterization of the minimum cycle mean in a digraph
    • R.M. Karp, A characterization of the minimum cycle mean in a digraph, Discrete Math. 23 (1978), pp. 309-311.
    • (1978) Discrete Math. , vol.23 , pp. 309-311
    • Karp, R.M.1
  • 24
    • 0002945715 scopus 로고
    • Linear operators leaving invariant a cone in a Banach space
    • in Russian, 1(23)
    • M.G. Krein and M.A. Rutman, Linear operators leaving invariant a cone in a Banach space (in Russian), Uspekhi Mat. Nauk 3:1(23) (1948), pp. 3-95.
    • (1948) Uspekhi Mat. Nauk , vol.3 , pp. 3-95
    • Krein, M.G.1    Rutman, M.A.2
  • 25
  • 26
    • 0000162636 scopus 로고
    • Sur les espaces complets
    • C. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), pp. 301-309.
    • (1930) Fund. Math. , vol.15 , pp. 301-309
    • Kuratowski, C.1
  • 27
    • 21444453228 scopus 로고    scopus 로고
    • Boundary layer phenomena for differential-delay equations with state dependent time lags: II
    • J. Mallet-Paret and R.D. Nussbaum, Boundary layer phenomena for differential-delay equations with state dependent time lags: II, J. Reine Angew. Math. 477 (1996), pp. 129-197.
    • (1996) J. Reine Angew. Math. , vol.477 , pp. 129-197
    • Mallet-Paret, J.1    Nussbaum, R.D.2
  • 30
    • 84972570025 scopus 로고
    • The radius of the essential spectrum
    • R.D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 38 (1970), pp. 473-478.
    • (1970) Duke Math. J. , vol.38 , pp. 473-478
    • Nussbaum, R.D.1
  • 31
    • 0001506862 scopus 로고
    • A generalization of the Ascoli theorem and an application to functional differential equations
    • R.D. Nussbaum, A generalization of the Ascoli theorem and an application to functional differential equations, J. Math. Anal. Appl. 35 (1971), pp. 600-610.
    • (1971) J. Math. Anal. Appl. , vol.35 , pp. 600-610
    • Nussbaum, R.D.1
  • 32
    • 0011508129 scopus 로고
    • Periodic solutions of some integral equations from the theory of epidemics
    • V. Lakshmikantham, editor, Academic Press, New York, 1977
    • R.D. Nussbaum, Periodic solutions of some integral equations from the theory of epidemics, in: Nonlinear Systems and Applications (Arlington, Texas, 1976), V. Lakshmikantham, editor, Academic Press, New York, 1977, pp. 235-255.
    • (1977) Nonlinear Systems and Applications (Arlington, Texas, 1976) , pp. 235-255
    • Nussbaum, R.D.1
  • 33
    • 0000984231 scopus 로고
    • Eigenvalues of nonlinear operators and the linear Krein-Rutman theorem
    • Fixed Point Theory (Sherbrooke, Quebec, 1980), E. Fadell and G. Fournier, editors, Springer-Verlag, Berlin
    • R.D. Nussbaum, Eigenvalues of nonlinear operators and the linear Krein-Rutman theorem, in: Fixed Point Theory (Sherbrooke, Quebec, 1980), E. Fadell and G. Fournier, editors, Lecture Notes in Mathematics 886, Springer-Verlag, Berlin, 1981, pp. 309-331.
    • (1981) Lecture Notes in Mathematics , vol.886 , pp. 309-331
    • Nussbaum, R.D.1
  • 34
    • 0011521813 scopus 로고
    • The Fixed Point Index and Some Applications
    • Presses de l'Univ, de Montréal, Montreal
    • R.D. Nussbaum, The Fixed Point Index and Some Applications, Séminaire de Mathématiques Supérieures 94, Presses de l'Univ, de Montréal, Montreal, 1985.
    • (1985) Séminaire de Mathématiques Supérieures , vol.94
    • Nussbaum, R.D.1
  • 35
    • 38249043835 scopus 로고
    • Convexity and log convexity for the spectral radius
    • R.D. Nussbaum, Convexity and log convexity for the spectral radius, Linear Alg. Appl. 73 (1986), pp. 59-112.
    • (1986) Linear Alg. Appl. , vol.73 , pp. 59-112
    • Nussbaum, R.D.1
  • 36
    • 0001338184 scopus 로고
    • Hilbert's projective metric and iterated nonlinear maps
    • R.D. Nussbaum, Hilbert's projective metric and iterated nonlinear maps, Memoirs Amer. Math. Soc. 75:391 (1988).
    • (1988) Memoirs Amer. Math. Soc. , vol.75 , pp. 391
    • Nussbaum, R.D.1
  • 37
    • 0001146015 scopus 로고
    • Iterated nonlinear maps and Hilbert's projective metric, II
    • R.D. Nussbaum, Iterated nonlinear maps and Hilbert's projective metric, II, Memoirs Amer. Math. Soc. 79:401 (1989).
    • (1989) Memoirs Amer. Math. Soc. , vol.79 , pp. 401
    • Nussbaum, R.D.1
  • 38
    • 0000653784 scopus 로고
    • Convergence of iterates of a nonlinear operator arising in statistical mechanics
    • R.D. Nussbaum, Convergence of iterates of a nonlinear operator arising in statistical mechanics, Nonlinearity 4 (1991), pp. 1223-1240.
    • (1991) Nonlinearity , vol.4 , pp. 1223-1240
    • Nussbaum, R.D.1
  • 39
    • 38248998696 scopus 로고
    • Entropy minimization, Hilbert's projective metric, and scaling integral kernels
    • R.D. Nussbaum, Entropy minimization, Hilbert's projective metric, and scaling integral kernels, J. Func. Anal. 115 (1993), pp. 45-99.
    • (1993) J. Func. Anal. , vol.115 , pp. 45-99
    • Nussbaum, R.D.1
  • 40
    • 0001574509 scopus 로고
    • Lattice isomorphisms and iterates of nonexpansive maps
    • R.D. Nussbaum, Lattice isomorphisms and iterates of nonexpansive maps, Nonlinear Anal. 22 (1994), pp. 945-970.
    • (1994) Nonlinear Anal. , vol.22 , pp. 945-970
    • Nussbaum, R.D.1
  • 41
    • 85008271908 scopus 로고
    • Nonlinear Perron-Frobenius problem on an ordered Banach space
    • T. Ogiwara, Nonlinear Perron-Frobenius problem on an ordered Banach space, Japan J. Math. 21 (1995), pp. 43-103.
    • (1995) Japan J. Math. , vol.21 , pp. 43-103
    • Ogiwara, T.1
  • 42
    • 0003342926 scopus 로고
    • Topological vector spaces
    • Springer-Verlag, New York
    • H.H. Schaefer, Topological Vector Spaces, Graduate Texts in Mathematics 3, Springer-Verlag, New York, 1971.
    • (1971) Graduate Texts in Mathematics , vol.3
    • Schaefer, H.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.