We consider nonlinear periodic systems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential function. In the right hand side forcing term, we have the combined effects of p-sublinear (concave) and p-superlinear (convex) terms. However, the p-superlinear term need not satisfy the Ambrosetti-Rabinowitz condition. By combining nonsmooth critical point theory with the Ekeland variational principle, we show that the system has at least two nontrivial periodic solutions.

Multiple solutions for nonlinear periodic systems with combined nonlinearities and a nonsmooth potential

PAPALINI, Francesca
2012

Abstract

We consider nonlinear periodic systems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential function. In the right hand side forcing term, we have the combined effects of p-sublinear (concave) and p-superlinear (convex) terms. However, the p-superlinear term need not satisfy the Ambrosetti-Rabinowitz condition. By combining nonsmooth critical point theory with the Ekeland variational principle, we show that the system has at least two nontrivial periodic solutions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/48309
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