Constant Sign and Nodal Solutions for Problems with the p-Laplacian and a Nonsmooth Potential Using Variational Techniques
نویسندگان
چکیده
We consider a nonlinear elliptic equation driven by the p-Laplacian with a nonsmooth potential hemivariational inequality and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second negative, and the third sign changing nodal solution . Our hypotheses on the nonsmooth potential incorporate in our framework of analysis the so-called asymptotically p-linear problems.
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