Existence of periodic solutions for nonlinear evolution equations with pseudo monotone operators
HTML articles powered by AMS MathViewer
- by Naoki Shioji
- Proc. Amer. Math. Soc. 125 (1997), 2921-2929
- DOI: https://doi.org/10.1090/S0002-9939-97-03984-1
- PDF | Request permission
Abstract:
In this paper, we study the existence of $T$-periodic solutions for the problem \[ u’ (t) +A(t)u(t) =0, \quad t\in \mathbb R, \] where $A(t)$ is a $T$-periodic, pseudo monotone mapping from a reflexive Banach space into its dual.References
- Herbert Amann, Periodic solutions of semilinear parabolic equations, Nonlinear analysis (collection of papers in honor of Erich H. Rothe), Academic Press, New York, 1978, pp. 1–29. MR 499089
- Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843
- Ronald I. Becker, Periodic solutions of semilinear equations of evolution of compact type, J. Math. Anal. Appl. 82 (1981), no. 1, 33–48. MR 626739, DOI 10.1016/0022-247X(81)90223-7
- Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188
- Radu Caşcaval and Ioan I. Vrabie, Existence of periodic solutions for a class of nonlinear evolution equations, Rev. Mat. Univ. Complut. Madrid 7 (1994), no. 2, 325–338. MR 1297518
- R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 0221256
- Jean-Pierre Gossez, Existence of periodic solutions for some first order nonlinear ordinary differential equations at resonance, Ordinary differential equations and functional equations (Florence, 1978), CNR, Rome, 1978, pp. 361–379. MR 690624
- Norimichi Hirano, Abstract nonlinear Volterra equations with positive kernels, SIAM J. Math. Anal. 17 (1986), no. 2, 403–414. MR 826701, DOI 10.1137/0517030
- Norimichi Hirano, Nonlinear Volterra equations with positive kernels, Nonlinear and convex analysis (Santa Barbara, Calif., 1985) Lecture Notes in Pure and Appl. Math., vol. 107, Dekker, New York, 1987, pp. 83–98. MR 892784
- Norimichi Hirano, Nonlinear evolution equations with nonmonotonic perturbations, Nonlinear Anal. 13 (1989), no. 6, 599–609. MR 998507, DOI 10.1016/0362-546X(89)90081-3
- Norimichi Hirano, Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces, Proc. Amer. Math. Soc. 120 (1994), no. 1, 185–192. MR 1174494, DOI 10.1090/S0002-9939-1994-1174494-8
- J. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conference Series in Mathematics, vol. 40, American Mathematical Society, Providence, R.I., 1979. Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 9–15, 1977. MR 525202
- Jan Prüss, Periodic solutions of semilinear evolution equations, Nonlinear Anal. 3 (1979), no. 5, 601–612. MR 541871, DOI 10.1016/0362-546X(79)90089-0
- Michael Renardy and Robert C. Rogers, An introduction to partial differential equations, Texts in Applied Mathematics, vol. 13, Springer-Verlag, New York, 1993. MR 1211418
- Ioan I. Vrabie, Periodic solutions for nonlinear evolution equations in a Banach space, Proc. Amer. Math. Soc. 109 (1990), no. 3, 653–661. MR 1015686, DOI 10.1090/S0002-9939-1990-1015686-4
- Eberhard Zeidler, Nonlinear functional analysis and its applications. II/A, Springer-Verlag, New York, 1990. Linear monotone operators; Translated from the German by the author and Leo F. Boron. MR 1033497, DOI 10.1007/978-1-4612-0985-0
- Eberhard Zeidler, Nonlinear functional analysis and its applications. II/B, Springer-Verlag, New York, 1990. Nonlinear monotone operators; Translated from the German by the author and Leo F. Boron. MR 1033498, DOI 10.1007/978-1-4612-0985-0
Bibliographic Information
- Naoki Shioji
- Affiliation: Faculty of Engineering, Tamagawa University, Tamagawa Gakuen, Machida, Tokyo 194, Japan
- Email: shioji@eng.tamagawa.ac.jp
- Received by editor(s): December 19, 1995
- Received by editor(s) in revised form: April 30, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2921-2929
- MSC (1991): Primary 47H05, 47H17, 47H30, 35B10, 35F25
- DOI: https://doi.org/10.1090/S0002-9939-97-03984-1
- MathSciNet review: 1402888