Existence and multiplicity of solutions for discontinuous non-local fractional elliptic problems
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This paper is concerned with a nonlocal fractional $p$-{\scriptsize Laplacian} problem with Dirichlet boundary condition. By using nonsmooth critical points theory and variational methods, we establish the existence and multiplicity theorems of solutions for this problem. These results presented here may be seen as an extension of some classical nonlinear analysis theorems to the case of fractional problems with discontinuous nonlinearity.
Abstract
This paper is concerned with a nonlocal fractional $p$-{\scriptsize Laplacian} problem with Dirichlet boundary condition. By using nonsmooth critical points theory and variational methods, we establish the existence and multiplicity theorems of solutions for this problem. These results presented here may be seen as an extension of some classical nonlinear analysis theorems to the case of fractional problems with discontinuous nonlinearity.