NODAL SOLUTIONS TO CRITICAL GROWTH ELLIPTIC PROBLEMS UNDER STEKLOV BOUNDARY CONDITIONS

被引：7

作者：

Berchio, Elvise ^{[1
]}

Gazzola, Filippo ^{[2
]}

Pierotti, Dario ^{[2
]}

机构：

[1] Univ Piemonte Orientale, Dipartimento SEMEQ, I-28100 Novara, Italy

[2] Dipartmento Matemat Politecn, I-20133 Milan, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 02期

关键词：

Critical growth; nodal solutions; Steklov; CRITICAL SOBOLEV EXPONENTS; EQUATIONS;

D O I：

10.3934/cpaa.2009.8.533

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study elliptic problems at critical growth under Steklov boundary conditions in bounded domains. For a second order problem we prove existence of nontrivial nodal solutions. These are obtained by combining a suitable linking argument with fine estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we obtain a multiplicity result by taking advantage of the explicit form of the Steklov eigenfunctions. We also partially extend the results in the ball to the case of fourth order Steklov boundary value problems.

引用

页码：533 / 557

页数：25

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