Existence of periodic solutions for nonlinear evolution equations with pseudo monotone operators

Proceedings of the American Mathematical Society

Volumn 125, Issue 10, 1997, Pages 2921-2929

  Shioji, Naoki ^a  

^a TAMAGAWA UNIVERSITY   (Japan)

Author keywords

Evolution equations; Periodic solutions; Pseudo monotone operators

Indexed keywords

EID: 21944441135     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03984-1     Document Type: Article

References (17)

1. H. Amann, Periodic solutions of semilinear parabolic equations, in Nonlinear analysis (A collection of papers in honor of Erich H. Rothe, Ed. L. Cesari, R. Kannan and H. F. Weinberger), 1-29, Academic Press, New York, 1978. MR 80a:35009
2. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976. MR 52:11666
3. R. I. Decker, Periodic solutions of semilinear equations of evolution of compact type, J. Math. Anal. Appl. 82 (1981), 33-48. MR 84a:34068
4. F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Symp. Pure Math. 18 part 2, 1976. MR 53:8982
5. J. P. Caşcaval and I. I. Vrabie, Existence of periodic solutions for a class of nonlinear evolution equations, Rev. Mate. Univ. Complutense Madrid 7 (1994), 325-338. MR 951:34113
6. R. E. Edwards, Functional analysis, Holt, Rinehart and Winston, New York, 1965. MR 30:4308
7. J. P. Gossez, Existence of periodic solutions for some first order ordinary differential equations, in Equadiff 78 (Convegno Internaz. Equaz. Diff. Ordin. ed Funzionali, R. Conti, G. Sestini and G. Villari ed.), Firenze, 1978, 361-379. MR 84m:34051
8. N. Hirano, Abstract nonlinear Volterra equations with positive kernels, SIAM J. Math. Anal. 17 (1986), 403-414. MR 87d:45028
9. N. Hirano, Nonlinear Volterra equations with positive kernels, in Nonlinear and convex analysis (Santa Barbara, Calif., 1985), Lecture Notes in Pure and Appl. Math., 107, 83-98, 1987. MR 88k:45004
10. N. Hirano, Nonlinear evolution equations with nonmonotonic perturbations, Nonlinear Anal. 13 (1989), 599-609. MR 90e:34114
11. N. Hirano, Existence of periodic solutions for nonlinear evolution equations in Hilbert space, Proc. Amer. Math. Soc. 120 (1994), 185-192. MR 94b:34087
12. J. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, 1979. MR 80c:47055
13. J. Prüss, Periodic solutions of semilinear evolution equations, Nonlinear Anal. 3 (1979), 221-235. MR 81a:34061
14. M. Renardy and R. C. Rogers, An introduction to partial differential equations, SpringerVerlag, New York, 1993. MR 94c:35001
15. I. I. Vrabie, Periodic solutions for nonlinear evolution equations in a Banach space, Proc. Amer. Math. Soc. 109 (1990), 653-661. MR 90k:34080
16. E. Zeidler, Nonlinear functional analysis and its applications II/A, Linear monotone operators, Springer-Verlag, New York, 1990. MR 91b:47001
17. E. Zeidler, Nonlinear functional analysis and its applications II/B, Nonlinear monotone operators, Springer-Verlag, New York, 1990. MR 91b:47002