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

Chao Nien Chen, Shyuh Yaur Tzeng

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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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All Science Journal Classification (ASJC) codes

  • Analysis

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