On the interior spike solutions for some singular perturbation problems
Juncheng Wei · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1998
For some singular perturbed Dirichlet and Neumann problems in a bounded smooth domain, we study solutions which have a spike in the interior. We obtain both necessary and sufficient conditions for the existence of interior spike solutions. We use, among others, the methods of projections and viscosity solutions, weak convergence of measures and Liapunov–Schmidt reduction.