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

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

arxiv.org/abs/math/0202106v1

Mathematics

Functional Analysis

Scientific paper

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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