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 (-Delta p)(s)u=lambda/u(gamma) vertical bar u(q);u > 0 in Omega with zero Dirichlet boundary condition. Here, Omega is an open bounded domain in R-N with smooth boundary, N > ps, s is an element of (0, 1), lambda > 0, 0 < gamma < 1, 1 < p < infinity, and p-1 < q <= p(s)(*) = Np/N-ps. We employ variational techniques to show the existence of multiple positive weak solutions of the above problem. We also prove that for some alpha is an element of (0, s], the weak solution to the problem is in C-1,C-alpha((Omega) over bar).