Solvability of Dirichlet problems for semilinear elliptic equations on certain domains

Zhiren Jin

Vol. 176 (1996), No. 1, 117–128

DOI: 10.2140/pjm.1996.176.117

Abstract

We demonstrate a method to solve Dirichlet problems for semilinear elliptic equations on certain domains by a combination of change of variables, variational method and super-sub- solutions method. We show that Dirichlet problems for a semilinear elliptic equation have a least one solution as long as a relationship between the growth rate of the nonlinear term and the size of the domain is satisfied. The result can be applied to semilinear elliptic equations with super-critical growth.

Mathematical Subject Classification 2000

Primary: 35J65

Milestones

Received: 31 August 1994

Revised: 26 January 1995

Published: 1 November 1996