Analysis and computation for a class of semilinear elliptic boundary value problems
In this paper, with the help of super-solutions and sub-solutions, we set up a general framework and get a positive threshold Lambda for solution existence and non-existence of a class of semilinear elliptic Dirichlet boundary value problems. Moreover, a result on multiplicity is obtained when lambda is large enough. We also give a numerical method to solve and visualize the positive solutions of the problem. Theoretical results are illustrated by numerical simulation. (C) 2012 Elsevier Ltd. All rights reserved.
super-solution multiple solutions bifurcation sub-solution pseudo-arclength continuation