Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems

Chao Nien Chen, Shyuh Yaur Tzeng

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied. To overcome this difficulty, we analyze Palais-Smale sequences, and use their convergence to justify the existence of critical points for a functional. We show the existence of positive solutions using a minimax method and comparison arguments for semilinear elliptic equations.

Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalElectronic Journal of Differential Equations
Volume1999
Publication statusPublished - 1999 May 14

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Palais-Smale Condition
Nonlinear Elliptic Boundary Value Problem
Minimax Methods
Semilinear Elliptic Equations
Elliptic Boundary Value Problems
Calculus of variations
Existence of Positive Solutions
Unbounded Domain
Justify
Critical point

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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abstract = "When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied. To overcome this difficulty, we analyze Palais-Smale sequences, and use their convergence to justify the existence of critical points for a functional. We show the existence of positive solutions using a minimax method and comparison arguments for semilinear elliptic equations.",
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Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems. / Chen, Chao Nien; Tzeng, Shyuh Yaur.

In: Electronic Journal of Differential Equations, Vol. 1999, 14.05.1999, p. 1-29.

Research output: Contribution to journalArticle

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