A nonsmooth variational approach to differential problems. A case study of nonresonance under the first eigenvalue for a strongly nonlinear elliptic problem

2002/02/12 by Youssef Jabri, Jabri, Youssef
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #math.FA #msc:35A15 #msc:35D05 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0202106

arxiv created 2002/02/12 · arxiv updated 2009/11/30

Abstract

We adapt a technique of nonsmooth critical point theory developed by Degiovanni-Zani for a semilinear problem involving the Laplacian to the the case of the p-Laplacian. We suppose only coercivity conditions on the potential and impose no growth condition of the nonlinearity. The coercivity is obtained using similar nonresonance conditions to [Mawhin-Ward-Willem] and to [Landesman-Lazer] in two different results and using some comparison functions and comparison spaces in a third one. It is also shown that neither of the three theorems implies the two others.

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