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

Electronic Journal of Qualitative Theory of Differential Equations

Maicon Sônego¹ 

[1] Universidade Federal de Itajubá, Itajubá, M.G., Brasil;

关键词: surface of revolution;    stability or instability of solutions;   

DOI  :  10.14232/ejqtde.2016.1.95

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown