Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution

Abstract

We consider the equation $\Delta u+f(u)=0$ on a surface of revolution with Dirichlet boundary conditions. We obtain conditions on $f$, the geometry of the surface and the maximum value of a positive solution in order to ensure its stability or instability. Applications are given for our main results.

Keywords

• surface of revolution
• stability or instability of solutions