On time-periodic solutions of some nonlinear parabolic equations with nonmonotone multivalued terms

Mitsuharu Otani, Vasile Staicu

DOI: http://dx.doi.org/10.12775/TMNA.2019.092


In this paper we study the existence of time periodic solutions to a class of nonlinear parabolic equations with multivalued nonlinear terms subject to the homogeneous Dirichlet boundary condition. We give two types of existence results: one for large periodic solutions with any large data, and the other for small periodic solutions with small data. Both concern the case where the nonlinear terms contain either a upper semicontinuous multivalued term or a lower semicontinuous multivalued term. Some applications of our results are also given.


time-periodic solutions; nonlinear parabolic equations; nonmonotone multivalued terms

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