Asymptotic Estimates and Qualitative Properties of an Elliptic Problem in Dimension Two-Reference-Cited by-同舟云学术

Asymptotic Estimates and Qualitative Properties of an Elliptic Problem in Dimension Two

Published:2004-02-01 Issue:1 Volume:4 Page:15-36
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

El Mehdi Khalil¹,Grossi Massimo²

Affiliation:

1. Faculte des Sciences et Techniques Universite de Nouakchott BP 5026, Nouakchott, Mauritania

2. Dipartimento di Matematica Universit´a di Roma ”La Sapienza” P.le A. Moro, Roma, Italia

Abstract

Abstract In this paper we study a semilinear elliptic problem on a bounded domain in ℝ2 with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymptotic estimates which enable us to associate a “limit problem” to the initial one. Using these estimates we prove some qualitative properties of the solutions, namely characterization of the level sets and nondegeneracy.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2004-0102/pdf

Reference12 articles.

1. On the uniqueness of the positive solution of a singularly perturbed problem Rocky Mount;Dancer;Math,1995

2. A note on the Sobolev inequality;Bianchi;Funct Anal,1991

3. On a two - dimensional elliptic problem with large exponent in nonlinearity;Ren;Trans,1994

4. A priori bounds for positive solutions of nonlinear elliptic equations;Gidas;Par Diff Eqns,1981

5. Symmetry and related properties via the maxi - mum principle;Gidas;Math Phys,1979

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