Periodic solutions for a class of second order delay systems (Q372884)

This paper deals with the existence of periodic solutions of the system \[ -u''(t)+Au(t) = f(t, u(t-r)), \] where \(A = (a_{ij})_{n\times n}\) is a symmetric matrix, \(r> 0\) is a constant, and \(f(t, x)\) is continuous and \(r\)-periodic in \(t\). Under some assumptions on \(A\) and \(f\), several theorems are proved by using the linking theory and variational methods for the existence and multiplicity of \(2r\)-periodic solutions.