Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity

Abstract

In this paper, we prove the existence of multiple weak solutions for a nonlinear nonlocal elliptic partial differential equation involving a singularity and a power nonlinearity, which is given as (-Δp)su=λuγ+uq;u>0 in ω with zero Dirichlet boundary condition. Here, ω is an open bounded domain in RN with smooth boundary, N > ps, s (0, 1), λ > 0, 0 < γ < 1, 1 < p < ∞, and p-1