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