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.