On the interior spike solutions for some singular perturbation problems
- 1 January 1998
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 128 (4) , 849-874
- https://doi.org/10.1017/s030821050002182x
Abstract
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.Keywords
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