Anti-periodic solutions for semilinear evolution equations

By Yuqing Chen. 2002

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In this paper, we use the homotopy method to establish the existence and uniqueness of anti-periodic solutions for the nonlinear anti-periodic problem � ˙ + A(t, x )+ Bx = f (t) a.e. t ∈ R, x(t + T )=- x(t), where A(t, x) is a nonlinear map and B is a bounded linear operator from R N to R N. Sufficient conditions for the existence of the solution set are presented. Also, we consider the nonlinear evolution problems with a perturbation term which is multivalued. We show that, for this problem, the solution set is nonempty and weakly compact in W 1,2 (I, R N ) for the case of convex valued perturbation and prove the existence theorems of anti-periodic solutions for the nonconvex case. All illustrative examples are provided.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/26c9d78ef46bdc35b7b1a06ccf400d3c11632d6c