EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS IN ESTEBAN-LIONS DOMAINS WITH HOLES

Abstract

In this article, we consider the semilinear elliptic equation $$(*)_\lambda \,\,\,\,\,\,\, -\Delta u+u=\lambda K(x)u^p+h(x)\mbox{ in }\Omega, u\gt 0\mbox{ in }\Omega\mbox{ }, u\in H_0^1(\Omega ), $$ where $\lambda \geq 0,$ $N\ge 2$, $1\lambda^*$. We also establish the asymptotic behavior and some further properties of positive solutions of equation $(*)_\lambda$.