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Solutions with boundary-layers and spike-layers to singularly perturbed quasilinear Dirichlet problems

โœ Scribed by Zongming Guo

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
369 KB
Volume
267
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

The structure of nontrivial nonnegative solutions to singularly perturbed quasilinear Dirichlet problems of the form

It is shown that there are many nontrivial nonnegative solutions with spike-layers. Moreover, the measure of each spike-layer is estimated as โ†’ 0 + . These results are applied to the study of the structure of positive solutions of the same problems with f changing sign many times in (0, โˆž). Uniqueness of a solution with a boundary-layer and many positive intermediate solutions with spike-layers are obtained for sufficiently small.

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