Some remarks on the stability of sign changing solutions

Abstract

In this paper, we study the stability of changing sign solutions of weakly nonlinear second order elliptic equations. Here by stability, we means stability for the natural corresponding parabolic problem. We prove the instability of many sign changing solutions. On the other hand, we find a number of methods for obtaining stable changing sign solutions. Some of these methods involve singular perturbations. © 1995 Tohoku University, Mathematical Institute.