Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains

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 that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super and sub-solution method. A super solution itself is constructed by solving a quasilinear elliptic equation via a modified Perron's method.

Keywords

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