Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators
KeywordsAnti-periodic solution, Hille--Yosida operator, measure of noncompactness, fixed point theory
AbstractIn this paper we are interested in the anti-periodic problem governed by a class of semilinear differential inclusions with linear parts generating integrated semigroups. By adopting the Lyapunov-Perron method and the fixed point argument for multivalued maps, we prove the existence of anti-periodic solutions. Furthermore, we study the long-time behavior of mild solutions in connection with anti-periodic solutions. Consequently, as the nonlinearity is of single-valued, we obtain the exponential stability of anti-periodic solutions. An application of theoretical results to a class of partial differential equations will be given.
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