Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces

Hirano, Norimichi

doi:10.1090/S0002-9939-1994-1174494-8

Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces
HTML articles powered by AMS MathViewer

by Norimichi Hirano PDF

Proc. Amer. Math. Soc. 120 (1994), 185-192 Request permission

Abstract:

In this paper, we consider the existence and multiplicity of periodic solutions of the problem $u’ + Au \ni g(t,u)$ where $A$ is a subdifferential of a convex function defined in a Hilbert space $H$ and $g:R \times H \to H$ is a Carathéodory function periodic with respect to the first variable.

References

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
Haïm Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 1, 115–175 (French). MR 270222

Operateurs maximaux monotones

Felix E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1100–1103. MR 177295, DOI 10.1073/pnas.53.5.1100
Klaus Deimling, Periodic solutions of differential equations in Banach spaces, Manuscripta Math. 24 (1978), no. 1, 31–44. MR 499551, DOI 10.1007/BF01168561
Norimichi Hirano, Existence of multiple periodic solutions for a semilinear evolution equation, Proc. Amer. Math. Soc. 106 (1989), no. 1, 107–114. MR 953007, DOI 10.1090/S0002-9939-1989-0953007-5
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
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
Ioan I. Vrabie, The nonlinear version of Pazy’s local existence theorem, Israel J. Math. 32 (1979), no. 2-3, 221–235. MR 531265, DOI 10.1007/BF02764918