Existence and nonexistence of solutions for a quasilinear elliptic system
Volume 113 / 2015
Annales Polonici Mathematici 113 (2015), 155-164
MSC: 35J65, 35J50.
DOI: 10.4064/ap113-2-3
Abstract
By a sub-super solution argument, we study the existence of positive solutions for the system $$\left\{\begin{array}{l@{\quad}l} -\varDelta_{p}u=a_{1}(x)F_{1}(x,u,v) &{\rm in}\ \varOmega,\\ -\varDelta_{q}v=a_{2}(x)F_{2}(x,u,v) &{\rm in}\ \varOmega,\\ u,v>0 &{\rm in}\ \varOmega,\\ u=v=0 &{\rm on}\ \partial\varOmega,\end{array}\right. $$ where $\varOmega$ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary or $\varOmega=\mathbb{R}^{N}$. A nonexistence result is obtained for radially symmetric solutions.
