Multiplicity of Positive Solutions for elliptic problem in Fractional Orlicz-Sobolev Spaces with Discontinuous Nonlinearities

Abstract

It is established existence and multiplicity of positive solutions for a non-local elliptic problem driven by
$(-\Delta)^s_{\mathrm{a}(\cdot)}$ operator, with Dirichlet-type boundary conditions. One of these solutions
is obtained as a critical point to the energy function associated with the studied elliptic problem by using the well-known
mountain pass theorem. The nonlinearities is not satisfied Ambrosetti-Rabinowitz condition, monotonocity or
convexity conditions, and can be discontinuous in nature.