Periodic solutions of second order nonautonomous systems with the potentials changing sign (Q1327573)

This paper is concerned with the following second order system \[ \ddot x + b(t) V'(x) = 0,\quad \text{for\;}x \in \mathbb{R}^ N, \] where \(V\in C^ 2(\mathbb{R}^ N,\mathbb{R})\) satisfies some superquadratic growth assumptions and \(b\) is a \(T\)-periodic continuous real function. Some existence results for periodic solutions of the above system are presented in Theorems 1 and 2 with positive and negative average values for \(b\), respectively. The proofs are based on the well-known techniques of critical point theory. The multiplicity results are given in Theorems 3 and 4, based on the consideration of the Nehari's manifold associated with the functional considered.