We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential function. First we establish an alternative minimax expression for the first nonzero eigenvalue for the negative periodic scalar p-Laplacian and then using it we prove the existence of three nontrivial solutions, two of which have constant sign. Our approach is variational based on the nonsmooth critical point theory.
On the existence of three nontrivial solutions for periodic problems driven by the scalar p-Laplacian / Papageorgiou, N., Papalini, F.. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 11 (2):(2011), pp. 455-471.
On the existence of three nontrivial solutions for periodic problems driven by the scalar p-Laplacian
PAPALINI, Francesca
2011-01-01
Abstract
We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential function. First we establish an alternative minimax expression for the first nonzero eigenvalue for the negative periodic scalar p-Laplacian and then using it we prove the existence of three nontrivial solutions, two of which have constant sign. Our approach is variational based on the nonsmooth critical point theory.File in questo prodotto:
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