Multiplicity of solutions for quasilinear elliptic systems with singularity. (English) Zbl 1316.35122
Summary: In this paper, we study the existence of multiple solutions for the following quasilinear elliptic system:
\[
\begin{cases} - \Delta_p u - \mu_1 \frac{|u|^{p - 2} u}{|x|^p} = \alpha_1 \frac{u^{p*(t) - 2}}{|x|^t}u + \beta_1 |v|^{\beta_2} |u|^{\beta_1 - 2_u},\quad & x \in \Omega, \\ - \Delta_q v - \mu_2 \frac{|v|^{q - 2} v}{|x|^q} = \alpha_2 \frac{v^{q*(s) - 2}}{|x|^s}v + \beta_2 |u|^{\beta_1} |v|^{\beta_2 - 2_u}, \quad & x \in \Omega, \\ u(x) = v(x) = 0, \quad & x \in \partial \Omega. \end{cases}
\]
Multiplicity of solutions for the quasilinear problem is obtained via variational method.
MSC:
| 35J50 | Variational methods for elliptic systems |
| 35J62 | Quasilinear elliptic equations |
| 35J48 | Higher-order elliptic systems |
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