Existence of positive solutions for Dirichlet problems of some singular elliptic equations

Abstract

When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations similar to the singular Emden-Fowler equation. The proof is based on a super and sub-solution method. A super solution is constructed by Perron's method together with a family of auxiliary functions.

Keywords

• Elliptic boundary value problems
• positive solutions
• singular semilinear equations
• unbounded domains
• Perron's method
• super solutions.