Existence, boundary behavior and asymptotic behavior of solutions to singular elliptic boundary-value problems

Abstract

In this article, we consider the singular elliptic boundary-value problem $$ -\Delta u+f(u)-u^{-\gamma} =\lambda u \text{ in } \Omega,\quad u>0\text{ in } \Omega,\quad u=0 \text{ on } \partial\Omega. $$ Using the upper-lower solution method, we show the existence and uniqueness of the solution. Also we study the boundary behavior and asymptotic behavior of the positive solutions.

Keywords

• 35J25, 35J60, 35J75