Existence and multiplicity results for a degenerate quasilinear elliptic system near resonance

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• 作者：Yu-Cheng An ; Xiong Lu ; Hong-Min Suo
• 关键词：degenerate elliptic system ; Ekeland’s variational principle ; mountain pass theorem ; saddle point theorem
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,188 KB
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• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

We establish existence and multiplicity results for weak solutions of a degenerate quasilinear elliptic system. By using Ekeland’s variational principle, the mountain pass theorem and the saddle point theorem in critical point theory, we obtain the existence of one or three solutions for an elliptic system with Dirichlet boundary conditions under some restriction on \(\lambda\) . This kind of results was firstly obtained by Mawhin and Schmitt (Ann. Pol. Math. 51:241-248, 1990) for a semilinear two-point boundary value problem.