A CONJECTURE ON MULTIPLE SOLUTIONS OF A NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEM: SOME NUMERICAL EVIDENCE

摘要

We investigate a conjecture regarding the number of solutions of a second order elliptic boundary value problem with an asymmetric nonlinearity. This investigation makes use of several computer assisted techniques. First, we compute approximate solutions using Newton's Iteration for small b and then use a continuation method to show that the number of solutions becomes large as b increases.