The Descending Flow Method and Existence of Solutions for a Class of Elliptic Equations

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• 作者：Marcelo Montenegro ; Adilson E. Presoto
• 关键词：Primary 35J60 ; Secondary 35J61 ; Gradient flow ; general Palais ; Smale condition ; invariant sets ; semilinear elliptic problem ; existence of multiple solutions
• 刊名：Milan Journal of Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：83
• 期：2
• 页码：313-326
• 全文大小：577 KB
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• 作者单位：Marcelo Montenegro (1)
  Adilson E. Presoto (2)
  
  1. Departamento de Matem谩tica, Universidade Estadual de Campinas, IMECC, Rua S茅rgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brasil
  2. Departamento de Matem谩tica, Universidade Federal de S茫o Carlos, Rodovia Washington Lus, Km 235, CEP 13565-905, S茫o Carlos, SP, Brasil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1424-9294

文摘

We minimize the energy functional on invariant sets by the minus gradient flow. We characterize invariant sets by this flow and we identify disjoint invariant sets in which the functional is bounded from below, leading us to get three distinct solutions: a positive, a negative and a sign-changing one. Keywords Gradient flow general Palais-Smale condition invariant sets semilinear elliptic problem existence of multiple solutions