## 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

### Keywords:

periodic solution; p-Laplace system; minimax methods
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### References:

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