On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity

Abstract

In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak solution for a parameter dependent singular nonlinearity and existence of multiple solution for purturbed singular nonlinearity. Our argument is based on the variational and approximation approach.

On the regularity theory for mixed local and nonlocal quasilinear elliptic equations

“…is investigated by Arora-Radulescu [4] to prove existence results. We also refer to Garain [41] for semilinear mixed probelms with purturbed singularity. The quasilinear case 1 < p < ∞ for the equation…”