Some New Results on Subquadratic Lane–Emden Elliptic Systems

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• 作者：Sara Barile ; Addolorata Salvatore
• 关键词：Nonlinear elliptic system of Lane–Emden type ; subquadratic growth ; fourth ; order elliptic equation ; variational tools ; compact imbeddings
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：14
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1660-5454
• 卷排序：14

文摘

We deal with a nonlinear elliptic weighted system of Lane–Emden type in \(\mathbb R^N\), \(N \ge 3\), by exploiting its equivalence with a fourth-order quasilinear elliptic equation involving a suitable “sublinear” term. By overcoming the loss of compactness of the problem with some compact imbeddings in weighted \(L^p\)-spaces, we establish existence and multiplicity results by means of a generalized Weierstrass Theorem and a variant of the Symmetric Mountain Pass Theorem stated by R. Kajikiya for subquadratic functionals. These results, which generalize previous ones stated by the same authors, apply in particular to a biharmonic equation under Navier conditions in \(\mathbb R^N\).