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Some existence results on periodic solutions of ordinary \(p\)-Laplacian systems. (English) Zbl 1154.34331

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.

MSC:

34C25 Periodic solutions to ordinary differential equations
47J30 Variational methods involving nonlinear operators
49J35 Existence of solutions for minimax problems
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