Anti-periodic solutions for semilinear evolution equations.
The authors study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation \[ \begin{cases} u'(t)+Au(t)+F(t,u(t))=0, &t\in\mathbb R\\ u(t+T)=-u(t), &t\in\mathbb R,\end{cases} \] in a Hilbert space \(H\), where \(A\) is a selfadjoint operator and \(F\) is a continuous nonlinear operator. An existence result is obtained under assumptions that \(D(A)\) is compactly embedded into \(H\) and \(F\) is anti-periodic and bounded by an \(L^2\) function. Furthermore, anti-periodic solutions for second-order equations are also studied.
scientific article; zbMATH DE number 1866589