Some existence results on periodic solutions of ordinary \(p\)-Laplacian systems (Q2370770)

Some existence theorems are obtained for periodic solutions of the ordinary \(p\)-Laplace system in \(\mathbb{R}^N\) \[ -(| u'| ^{p-2}u')' = \nabla F(t,u), \] assuming that \(F(\cdot, u)\) satisfies some coercivity type conditions in \(\mathbb{R}^N\) and grows strictly less than \(| u| ^p\). The method of proof is based on the Rabinowitz's Saddle Point Theorem.