Multiplicity of solutions for quasilinear elliptic systems with singularity

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• 作者：Juan Li (1)
  Yu-xia Tong (2)
  
  1. Department of Mathematics ; Ningbo University ; Ningbo ; 315211 ; China
  2. College of Science ; Heibei United University ; Tangshan ; 063009 ; China
  
• 关键词：quasilinear elliptic system ; singularity ; critical growth ; 35J60
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：31
• 期：1
• 页码：277-286
• 全文大小：253 KB
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• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

In this paper, we study the existence of multiple solutions for the following quasilinear elliptic system: $\left\{ \begin{gathered} - \Delta _p u - \mu _1 \frac{{|u|^{p - 2} u}} {{|x|^p }} = \alpha _1 \frac{{u^{p*(t) - 2} }} {{|x|^t }}u + \beta _1 |v|^{\beta _2 } |u|^{\beta _1 - 2_u } ,x \in \Omega , \hfill \\ - \Delta _q v - \mu _2 \frac{{|v|^{q - 2} v}} {{|x|^q }} = \alpha _2 \frac{{v^{q*(s) - 2} }} {{|x|^s }}v + \beta _2 |u|^{\beta _1 } |v|^{\beta _2 - 2_u } ,x \in \Omega , \hfill \\ u(x) = v(x) = 0, \hfill \\ \end{gathered} \right. $ Multiplicity of solutions for the quasilinear problem is obtained via variational method.