Existence of solution for a general class of elliptic equations with exponential growth

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• 作者：Anderson L. A. de Araujo ; Marcelo Montenegro
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：195
• 期：5
• 页码：1737-1748
• 全文大小：432 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891
• 卷排序：195

文摘

We use Galerkin approximations to show the existence of solution for a class of elliptic equations on bounded domains in \(\mathbb {R}^2\) with subcritical or critical exponential nonlinearities. We are able to solve the problem under more general assumptions usually assumed in the variational the approach, but not in our paper.KeywordsDirichlet problemGalerkin approximationTrudinger–Moser inequalityExponential growthConformal geometry