In 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.
"Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators." Topol. Methods Nonlinear Anal. 58 (1) 275 - 305, 2021. https://doi.org/10.12775/TMNA.2021.010