Antiperiodic solutions for semilinear evolution equations (Q1776477)

The authors investigate the semilinear evolution problem \[ u'(t)+Au(t)+\partial Gu(t)+F(t,u(t))=0,\text{ a.e. }t\in \mathbb R, \quad u(t+T)=-u(t),\;t\in \mathbb{R},\tag{P} \] in a Hilbert space \(H\), where \(A\) is a linear selfadjoint operator and \(\partial G\) is the subdifferential of~\(G\). Under suitable assumptions on \(A\), \(G\) and \(F\), the existence of a weak solution to (P) is proved. Applications to ordinary differential equations and partial differential equations are also presented.