Geodesic
On the existence of five nontrivial solutions for resonant problems with p-Laplacian
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 169-189.

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In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of (-Δₚ,W₀^1,p(Z)). We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
Keywords: p-Laplacian, Clarke subdifferential, linking sets, upper-lower solutions, second eigenvalue, nodal and constant sign solutions, second deformation theorem 
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Gasiński, Leszek; Papageorgiou, Nikolaos. On the existence of five nontrivial solutions for resonant problems with p-Laplacian. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 169-189. http://geodesic.mathdoc.fr/item/DMDICO_2010_30_2_a0/

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