Bounded solutions of second-order systems of differential equations (Q1399361)

The author considers the second-order vector differential equation \[ y''+ Cy'+ Ay+ F(y)= p(t),\tag{1} \] where \(C\), \(A\) are constant \(n\times n\)-matrices, \(F: \mathbb{R}^n\to \mathbb{R}^n\) is continuous and \(p: \mathbb{R}\to \mathbb{R}^n\) is continuous and bounded. Sufficient conditions for the existence of solutions to (1) bounded on \(\mathbb{R}\) are derived.