High energy solutions and nontrivial solutions for fourth-order elliptic equations

In this paper, we study the existence of nontrivial solutions and infinitely many high energy solutions for a class of nonlinear fourth-order elliptic equations in R N via variational methods. Three main theorems are obtained.

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 375; no. 2; pp. 699 - 705
Main Authors Yin, Yuling, Wu, Xian
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.03.2011
Elsevier
Subjects
Calculus of variations and optimal control
Critical point
Exact sciences and technology
High energy solutions
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Palais–Smale condition
Partial differential equations
Sciences and techniques of general use
Sobolev's embedding
Critical point
Palais–Smale condition
Sobolev's embedding
High energy solutions
Non linear equation
Energy
Variational methods
Mathematical analysis
Existence of solution
Sobolev embedding
Palais-Smale condition
Fourth order equation
Palais Smale condition
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Summary:In this paper, we study the existence of nontrivial solutions and infinitely many high energy solutions for a class of nonlinear fourth-order elliptic equations in R N via variational methods. Three main theorems are obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.10.019