Title | PERIODIC SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS WITH SMALL PERTURBATIONS |
Publication Type | Journal Article |
Year of Publication | 2005 |
Authors | Chen, YQ |
Secondary Authors | Cho, YJ, Kang, SM |
Secondary Title | Communications in Applied Analysis |
Volume | 9 |
Issue | 1 |
Start Page | 33 |
Pagination | 41 |
Date Published | 01/2005 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 34C25, 34G20, 47H05, 47H10 |
Abstract | Let A : R × E → E∗ be a limit mapping of class (S+ ), where E is a real reflexive Banach space. We study the existence of periodic solutions of the following evolution equation
As a special case, we derive the existence of periodic solutions when A is pseudomonotone.
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URL | http://www.acadsol.eu/en/articles/9/1/3.pdf |
Short Title | Periodic Solutions for Evolution Equations |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] H. Amann, Dynamic theory of quasilinear parabolic equations, I. Abstract evolution equations, Non. Anal., 12 (1988), 895-919.
[2] J. P. Aubin, I. Ekland, Applied Nonlinear Analysis, John Wiley & Sons, 1984. [3] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Groningen, 1976. [4] J. Berkovits and V. Mustonen, Monotonicity methods for nonlinear evolution equations, Non. Anal., 27 (1996), 1397-1405. [5] J. Berkovits, V. Mustonen, Topological degree for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems, Rc. Mat., Serie VII, 12 (1992), 597-621. [6] F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution, Proc. Symp. Pure Math., 18, Part 2, Amer. Math. Soc., Providence, RI, 1976. [7] F. E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc., 9 (1983), 1-39. [8] F. E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. USA., 53 (1965), 1100-1103. [9] S. S. Chang, Y. Q. Chen and B. S. Lee, Some existence theorems for differential inclusions in Hilbert spaces, Bull. Austral. Math. Soc., 54 (1996), 317-327. [10] Y. Q. Chen, Periodic solutions for evolution equations in Hilbert spaces, Yokohama Math. J., 44 (1997), 43-53. [11] M. G. Crandall and P. E. Souganidis, On nonlinear equations of evolution, Non. Anal., 13 (1989), 1375-1392. [12] K. Deimling, Periodic solutions of differential equations in Banach spaces, Manuscript Math., 24 (1978), 31-44.
[13] N. Hirano, Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces, Proc. Amer. Math. Soc., 120 (1994), 185-192. [14] T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, in Spectral Theory and Differential Equations, Lect. Notes Math., 448, 25-70, Springer-Verlag, 1975. [15] T. Kato, Linear and quasi-linear equations of evolution of hyperbolic type, C.I.M.E. II Ciclo, Hyperbolicity (1976), 125-191. [16] J. Pruss, Periodic solutions of semilinear evolution equations, Non. Anal., 3 (1979), 221-235. [17] N. Shioji, Existence of periodic solutions for nonlinear evolution equations with pseudo monotone operators, Proc. Amer. Math. Soc., 125 (1997), 2921-2929. [18] I. Vrabie, Periodic solutions for nonlinear evolution equations in a Banach space, Proc. Amer. Math. Soc., 109 (1990), 653-661.
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