Multiplicity of solutions for quasilinear elliptic systems with singularity
Multiplicity of solutions for quasilinear elliptic systems with singularity
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DOI：
10.1007/s10255-015-0466-4
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发表时间：
2015-01
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影响因子：
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通讯作者：
Juan Li;Yu-xia Tong
中科院分区：
文献类型：
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作者：
Juan Li;Yu-xia Tong
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.
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.