On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators

AbstractThe existence of anti-periodic solutions, hence also that of periodic solutions, to the nonlinear parabolic-type evolution equation (ddt)u(t)+∂ϑ(u(t))+F(t)u(t)∋0, t∈R is shown under the assumptions that the subdifferential operator ∂ϑ is odd and that {∂ϑ+F(t);t∈R} is a family of monotone operators satisfying the anti-periodicity condition F(t+T)(−v)-−F(t)v, v∈D(F(t)) (hence, {∂ϑ+F(t+T)}(−v)=−{∂ϑ+F(t)}v, v∈D(∂ϑ)∩D(F(t))), T∈:R, for a fixed T∈:R. Here coerciveness of ∂ϑ is not assumed. An application to a heat equation is given without assuming boundedness of the domain of Rxn