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

TL;DR

This paper investigates a class of mixed local and nonlocal semilinear elliptic equations with singular nonlinearities, establishing existence results for solutions using variational and approximation methods.

Contribution

It introduces new existence results for solutions of mixed local and nonlocal elliptic equations with singular nonlinearities, including multiple solutions under perturbations.

Findings

Existence of at least one weak solution for parameter-dependent singular nonlinearity.

Existence of multiple solutions for perturbed singular nonlinearity.

Application of variational and approximation techniques to singular elliptic problems.

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.