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Volumn 348, Issue 5, 1996, Pages 1663-1707

New results in the perturbation theory of maximal monotone and M-accretive operators in banach spaces

Author keywords

Compact perturbation; Compact resolvent; Degree theory; Eigenvalues for nonlinear operators; Fixed point theory; M accretive operator; Maximal monotone operator

Indexed keywords


EID: 21344432497     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01654-6     Document Type: Article
Times cited : (36)

References (41)
  • 1
    • 0041884992 scopus 로고
    • On the solution of nonlinear equations with monotone operators in a Banach space
    • MR 51:6512
    • Y. I. Alber, On the solution of nonlinear equations with monotone operators in a Banach space, Siberian Math. J. 16 (1975), 3-11. MR 51:6512
    • (1975) Siberian Math. J. , vol.16 , pp. 3-11
    • Alber, Y.I.1
  • 2
    • 0003478998 scopus 로고
    • Nonlinear Semigroups and Differential Equations in Banach Spaces
    • Leyden (The Netherlands), MR 52:11666
    • V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Int. Publ., Leyden (The Netherlands), 1975. MR 52:11666
    • (1975) Noordhoff Int. Publ.
    • Barbu, V.1
  • 4
    • 84980140308 scopus 로고
    • Perturbations of nonlinear maximal monotone sets in Banach space
    • MR 41:2454
    • H. Brézis, M. G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl Math. 23 (1970), 123-144. MR 41:2454
    • (1970) Comm. Pure Appl Math. , vol.23 , pp. 123-144
    • Brézis, H.1    Crandall, M.G.2    Pazy, A.3
  • 5
    • 0002747662 scopus 로고
    • Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces
    • Amer. Math. Soc., Providence, MR 53:8982
    • F. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symp. Pure Appl. Math., 18, Part 2, Amer. Math. Soc., Providence, 1976. MR 53:8982
    • (1976) Proc. Symp. Pure Appl. Math. , vol.18 , Issue.2 PART
    • Browder, F.1
  • 6
    • 0001782146 scopus 로고
    • p-spaces and sums of ranges of accretive operators
    • MR 80i:35083
    • p-spaces and sums of ranges of accretive operators, Nonlinear Anal. 2 (1978), 1-26. MR 80i:35083
    • (1978) Nonlinear Anal. , vol.2 , pp. 1-26
    • Calvert, B.D.1    Gupta, C.P.2
  • 7
    • 0003367410 scopus 로고
    • Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems
    • Boston, MR 91m:46021
    • I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Acad. Publ., Boston, 1990. MR 91m:46021
    • (1990) Kluwer Acad. Publ.
    • Cioranescu, I.1
  • 8
    • 0001399612 scopus 로고
    • Zeros of accretive operators
    • MR 50:3030
    • K. Deimling, Zeros of accretive operators, Manuscr. Math. 13 (1974), 365-374. MR 50:3030
    • (1974) Manuscr. Math. , vol.13 , pp. 365-374
    • Deimling, K.1
  • 10
    • 33645905692 scopus 로고
    • Nonzero solutions of nonlinear equations involving compact perturbations of accretive operators in Banach spaces
    • Z. Ding and A. G. Kartsatos, Nonzero solutions of nonlinear equations involving compact perturbations of accretive operators in Banach spaces, Nonlinear Anal. 25 (1995), 1333-1342.
    • (1995) Nonlinear Anal. , vol.25 , pp. 1333-1342
    • Ding, Z.1    Kartsatos, A.G.2
  • 11
    • 33645939890 scopus 로고    scopus 로고
    • P-Regular mappings and alternative results for perturbations of m-accretive operators in Banach spaces
    • (to appear)
    • Z. Ding and A. G. Kartsatos, P-Regular mappings and alternative results for perturbations of m-accretive operators in Banach spaces, Topol. Meth. Nonl. Anal, (to appear).
    • Topol. Meth. Nonl. Anal
    • Ding, Z.1    Kartsatos, A.G.2
  • 12
    • 0002871298 scopus 로고
    • On the nonlinear eigenvalue problem T(u) = λC(u) involving noncompact abstract and differential operators
    • MR 80b:47083
    • P. M. Fitzpatrick and W. V. Petryshyn, On the nonlinear eigenvalue problem T(u) = λC(u) involving noncompact abstract and differential operators, Boll. Un. Mat. Ital. B (5) 15 (1978), 80-107. MR 80b:47083
    • (1978) Boll. Un. Mat. Ital. B (5) , vol.15 , pp. 80-107
    • Fitzpatrick, P.M.1    Petryshyn, W.V.2
  • 13
    • 30244450140 scopus 로고
    • Ranges of operators of monotone type in Banach spaces
    • MR 95b:47068
    • Z. Guan, Ranges of operators of monotone type in Banach spaces, J. Math. Anal. Appl. 174 (1993), 256-264. MR 95b:47068
    • (1993) J. Math. Anal. Appl. , vol.174 , pp. 256-264
    • Guan, Z.1
  • 14
    • 1542644170 scopus 로고
    • Solvability of semilinear equations with compact perturbations of operators of monotone type
    • MR 94g:47080
    • Z. Guan, Solvability of semilinear equations with compact perturbations of operators of monotone type, Proc. Amer. Math. Soc. 121 (1994), 93-102. MR 94g:47080
    • (1994) Proc. Amer. Math. Soc. , vol.121 , pp. 93-102
    • Guan, Z.1
  • 15
    • 0342900176 scopus 로고
    • Solvability of nonlinear equations with coercivity generated by compact perturbations of m-accretive operators in Banach spaces
    • CMP 95:12
    • Z. Guan and A. G. Kartsatos, Solvability of nonlinear equations with coercivity generated by compact perturbations of m-accretive operators in Banach spaces, Houston J. Math. 21 (1995), 149-188. CMP 95:12
    • (1995) Houston J. Math. , vol.21 , pp. 149-188
    • Guan, Z.1    Kartsatos, A.G.2
  • 16
    • 33645955862 scopus 로고    scopus 로고
    • On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in Banach spaces
    • (to appear)
    • Z. Guan and A. G. Kartsatos, On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in Banach spaces, Nonlinear Anal, (to appear).
    • Nonlinear Anal
    • Guan, Z.1    Kartsatos, A.G.2
  • 17
    • 0013387256 scopus 로고
    • Ranges of perturbed maximal monotone and m-accretive operators in Banach spaces
    • MR 95i:47096
    • Z. Guan and A. G. Kartsatos, Ranges of perturbed maximal monotone and m-accretive operators in Banach spaces, Trans. Amer. Math. Soc. 347 (1995), 2403-2435. MR 95i:47096
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 2403-2435
    • Guan, Z.1    Kartsatos, A.G.2
  • 18
    • 0013534769 scopus 로고
    • Existence theorems for nonlinear noncoercive operator equations and nonlinear elliptic boundary value problems
    • MR 57:13600
    • C. P. Gupta and P. Hess, Existence theorems for nonlinear noncoercive operator equations and nonlinear elliptic boundary value problems, J. Diff. Eq. 22 (1976), 305-313. MR 57:13600
    • (1976) J. Diff. Eq. , vol.22 , pp. 305-313
    • Gupta, C.P.1    Hess, P.2
  • 19
    • 33645937574 scopus 로고    scopus 로고
    • On perturbations of m-accretive operators in Banach spaces
    • (to appear)
    • N. Hirano and A. K. Kalinde, On perturbations of m-accretive operators in Banach spaces, Proc. Amer. Math. Soc. (to appear).
    • Proc. Amer. Math. Soc.
    • Hirano, N.1    Kalinde, A.K.2
  • 20
    • 0028407841 scopus 로고
    • Ranges of sums and control of nonlinear evolutions with preassigned responses
    • CMP 94:12
    • D. R. Kaplan and A. G. Kartsatos, Ranges of sums and control of nonlinear evolutions with preassigned responses, J. Optim. Theory Appl. 81 (1994), 121-141. CMP 94:12
    • (1994) J. Optim. Theory Appl. , vol.81 , pp. 121-141
    • Kaplan, D.R.1    Kartsatos, A.G.2
  • 21
    • 0002290362 scopus 로고
    • Zeros of demicontinuous accretive operators in reflexive Banach spaces
    • MR 86j:47078
    • A. G. Kartsatos, Zeros of demicontinuous accretive operators in reflexive Banach spaces, Integral Equations 8 (1985), 175-184. MR 86j:47078
    • (1985) Integral Equations , vol.8 , pp. 175-184
    • Kartsatos, A.G.1
  • 22
    • 0011524287 scopus 로고
    • On compact perturbations and compact resolvents of nonlinear m-accretive operators in Banach spaces
    • MR 94c:47076
    • A. G. Kartsatbs, On compact perturbations and compact resolvents of nonlinear m-accretive operators in Banach spaces, Proc. Amer. Math. Soc. 119 (1993), 1189-1199. MR 94c:47076
    • (1993) Proc. Amer. Math. Soc. , vol.119 , pp. 1189-1199
    • Kartsatbs, A.G.1
  • 23
    • 0041514046 scopus 로고
    • Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces
    • Tampa, Florida, 1992, Walter De Gruyter, New York
    • A. G. Kartsatos, Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces, Proceedings of the First World Congress of Nonlinear Analysts, Tampa, Florida, 1992, Walter De Gruyter, New York, (1995), pp. 2197-2222.
    • (1995) Proceedings of the First World Congress of Nonlinear Analysts , pp. 2197-2222
    • Kartsatos, A.G.1
  • 24
    • 84966228526 scopus 로고
    • Sets in the ranges of sums for perturbations of nonlinear m-accretive operators in Banach spaces
    • MR 95c:47072
    • A. G. Kartsatos, Sets in the ranges of sums for perturbations of nonlinear m-accretive operators in Banach spaces, Proc. Amer. Math. Soc. 123 (1995), 145-156. MR 95c:47072
    • (1995) Proc. Amer. Math. Soc. , vol.123 , pp. 145-156
    • Kartsatos, A.G.1
  • 25
    • 0041514045 scopus 로고
    • On the construction of methods of lines for functional evolutions in general Banach spaces
    • A. G. Kartsatos, On the construction of methods of lines for functional evolutions in general Banach spaces, Nonlinear Anal. 25 (1995), 1321-1331.
    • (1995) Nonlinear Anal. , vol.25 , pp. 1321-1331
    • Kartsatos, A.G.1
  • 26
    • 0008527009 scopus 로고
    • A compact evolution operator generated by a time-dependent m-accretive operator in a general Banach space
    • CMP 95:15
    • A. G. Kartsatos, A compact evolution operator generated by a time-dependent m-accretive operator in a general Banach space, Math. Ann. 302 (1995), 473-487. CMP 95:15
    • (1995) Math. Ann. , vol.302 , pp. 473-487
    • Kartsatos, A.G.1
  • 27
    • 0001481713 scopus 로고
    • Sets in the ranges of nonlinear accretive operators in Banach spaces
    • CMP 95:14
    • A. G. Kartsatos, Sets in the ranges of nonlinear accretive operators in Banach spaces, Studia Math. 114 (1995), 261-273. CMP 95:14
    • (1995) Studia Math. , vol.114 , pp. 261-273
    • Kartsatos, A.G.1
  • 28
    • 33645926312 scopus 로고    scopus 로고
    • On the perturbation theory of m-accretive operators in Banach spaces
    • (to appear)
    • A. G. Kartsatos, On the perturbation theory of m-accretive operators in Banach spaces, Proc. Amer. Math. Soc. (to appear).
    • Proc. Amer. Math. Soc.
    • Kartsatos, A.G.1
  • 29
    • 0042920869 scopus 로고
    • Nonlinear equations involving compact perturbations of m-accretive operators in Banach spaces
    • CMP 95:7
    • A. G. Kartsatos and X. Liu, Nonlinear equations involving compact perturbations of m-accretive operators in Banach spaces, Nonlinear Anal. 24 (1995), 469-492. CMP 95:7
    • (1995) Nonlinear Anal. , vol.24 , pp. 469-492
    • Kartsatos, A.G.1    Liu, X.2
  • 30
    • 0023421999 scopus 로고
    • Controlling the space with pre-assigned responses, 3
    • MR 88j:49024
    • A. G. Kartsatos and R. D. Mabry, Controlling the space with pre-assigned responses, 3. Optim. Theory Appl. 54 (1987), 517-540. MR 88j:49024
    • (1987) Optim. Theory Appl. , vol.54 , pp. 517-540
    • Kartsatos, A.G.1    Mabry, R.D.2
  • 32
    • 0004081871 scopus 로고
    • Cambridge Univ. Press, Cambridge, MR 58:12558
    • N. G. Lloyd, Degree Theory, Cambridge Univ. Press, Cambridge, 1978. MR 58:12558
    • (1978) Degree Theory
    • Lloyd, N.G.1
  • 33
    • 0011622187 scopus 로고
    • Positive eigenvectors of k-set contractions
    • MR 80b:47073
    • I. Massabo and C. A. Stuart, Positive eigenvectors of k-set contractions, Nonlinear Anal. 3 (1979), 35-44. MR 80b:47073
    • (1979) Nonlinear Anal. , vol.3 , pp. 35-44
    • Massabo, I.1    Stuart, C.A.2
  • 34
    • 0001575687 scopus 로고
    • Degree of mapping in convex linear topological spaces
    • MR 13:150b
    • M. Nagumo, Degree of mapping in convex linear topological spaces, Amer. J. Math. 73 (1951), 497-511. MR 13:150b
    • (1951) Amer. J. Math. , vol.73 , pp. 497-511
    • Nagumo, M.1
  • 36
    • 0000847472 scopus 로고
    • Extension problems for accretive sets in Banach spaces
    • MR 57:17393
    • S. Reich, Extension problems for accretive sets in Banach spaces, J. Funct. Anal. 26 (1977), 378-395. MR 57:17393
    • (1977) J. Funct. Anal. , vol.26 , pp. 378-395
    • Reich, S.1
  • 37
    • 22244434526 scopus 로고
    • Introduction to Various Aspects of Degree Theory in Banach Spaces
    • A.M.S., Providence, MR 87m:47145
    • E. H. Rothe, Introduction to Various Aspects of Degree Theory in Banach Spaces, Math. Surveys and Monographs, 23, A.M.S., Providence, 1986. MR 87m:47145
    • (1986) Math. Surveys and Monographs , vol.23
    • Rothe, E.H.1
  • 38
    • 0003213458 scopus 로고
    • Methods for Analysis of Nonlinear Elliptic Boundary Value Problems
    • A.M.S., Providence, MR 95i:35109
    • I. V. Skrypnik, Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, Transl. Math. Monographs, 139, A.M.S., Providence, 1994. MR 95i:35109
    • (1994) Transl. Math. Monographs , vol.139
    • Skrypnik, I.V.1
  • 40
    • 0003892028 scopus 로고
    • Compactness Methods in Nonlinear Evolutions
    • London, MR 90f:47101
    • I. I. Vrabie, Compactness Methods in Nonlinear Evolutions, Longman Sci. Tech., London, 1987. MR 90f:47101
    • (1987) Longman Sci. Tech.
    • Vrabie, I.I.1


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