Anti-periodic solutions for evolution equations associated with monotone type mappings

In this work we study the anti-periodic problem {x′(t)∈−∂ϕx(t)−∂Gx(t)+f(t),a.e. t∈R,x(t)=−x(t+T),t∈R in a separable Hilbert space where ϕ:D(ϕ)⊆H→(−∞,+∞]ϕ:D(ϕ)⊆H→(−∞,+∞] is an even lower semi-continuous convex function, G:H→RG:H→R is an even continuous differentiable function such that ∂G∂G is a demi-continuous mapping of class (S+)(S+) or pseudo-monotone and f:R→Hf:R→H is a continuous mapping satisfying f(t+T)=−f(t)f(t+T)=−f(t) for t∈Rt∈R. Two existence results are obtained.