Abstract
Following a recent work of H. Okochi in the case of evolution equations generated by subdifferential operators in a real Hilbert space, we point out that many quasi-autonomous evolution equations of non monotone type associated to odd non linear operators have some anti-periodic solutions provided the forcing term is anti-periodic. This comes from the fact that the space of anti-periodic functions is transversal to the kernel of the linear part and stable under the action of odd non linear operators. The proofs of our results combine strong a priori estimates which depend very little on the non-linearities with an application of Schauder's fixed point theorem to some related dissipative equations.
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Haraux, A. Anti-periodic solutions of some nonlinear evolution equations. Manuscripta Math 63, 479–505 (1989). https://doi.org/10.1007/BF01171760
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DOI: https://doi.org/10.1007/BF01171760