Periodic solutions for evolution equations

Authors

  • Mihai Bostan Univ. de Franche-Comte, France.

DOI:

https://doi.org/10.58997/ejde.mon.03

Abstract

We study the existence and uniqueness of periodic solutions for evolution equations. First we analyze the one-dimensional case. Then for arbitrary dimensions (finite or not), we consider linear symmetric operators. We also prove the same results for non-linear sub-differential operators \(A = \partial \varphi\) where \(\varphi\) is convex.

For more information see https://ejde.math.txstate.edu/Monographs/03/abstr.html

References

V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordho (1976).

M. Bostan, Solutions periodiques des equations d' evolution, C. R. Acad. Sci. Paris, Ser. I Math. t.332, pp. 1-4, Equations derivees partielles, (2001).

M. Bostan, Almost periodic solutions for evolution equations, article in preparation.

H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Noth-Holland, Lecture Notes no. 5 (1972).

H. Brezis, A Haraux, Image d'une somme d'operateurs monotones et applications, Israel J. Math. 23 (1976), 2, pp. 165-186.

H. Brezis, Analyse fonctionnelle, Masson, (1998).

A. Haraux, Equations d' evolution non lineaires: solutions bornees periodiques, Ann. Inst. Fourier 28 (1978), 2, pp. 202-220.

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Published

2002-05-14

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Section

Monographs

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How to Cite

Periodic solutions for evolution equations. (2002). Electronic Journal of Differential Equations, 1(Mon. 01-09), Mon. 03, 1-41. https://doi.org/10.58997/ejde.mon.03