Classification of finite energy solutions to the fractional Lane–Emden–Fowler equations with slightly subcritical exponents

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• 作者：Woocheol Choi ; Seunghyeok Kim
• 关键词：Fractional Laplacian ; Critical nonlinearity ; Multi ; peak solutions ; Blow ; up analysis
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：269-308
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

We study qualitative properties of solutions to the fractional Lane–Emden–Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined in terms of either the spectra of the Dirichlet Laplacian or the integral representation. As a consequence, we classify the asymptotic behavior of all finite energy solutions. Our method also provides a simple and unified approach to deal with the classical (local) Lane–Emden–Fowler equation for any dimension \({>}2\).