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Counting Peaks of Solutions to Some Quasilinear Elliptic Equations with Large Exponents

โœ Scribed by X.F. Ren; J.C. Wei

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
558 KB
Volume
117
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

We consider the asymptotic behavior of certain solutions to a quasilinear problem with large exponent in the nonlinearity. Starting with the investigation of a Sobolev embedding, we get a sharp estimate for the embedding constant. Then we obtain a crucial (L^{\prime})-estimate for the (N)-Laplacian operators in (R^{*}). Using these estimates we prove that the solutions obtained by the standard variational method will develop a spiky pattern of peaks as the nonlincar exponent gets large, and we also have an upper bound depending on (N) only of the number of peaks. Stronger results for some special convex domains and some special solutions are also achieved. ' 1995 Academic Press. Inc.

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