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Existence and nonexistence of solutions for a quasilinear elliptic system

Volume 113 / 2015

Qin Li, Zuodong Yang 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.

Authors

  • Qin LiInstitute of Mathematics
    School of Mathematical Sciences
    Nanjing Normal University
    Jiangsu Nanjing 210023, China
    e-mail
  • Zuodong YangInstitute of Mathematics
    School of Mathematical Sciences
    Nanjing Normal University
    Jiangsu Nanjing 210023, China
    and
    School of Teacher Education
    Nanjing Normal University
    Jiangsu Nanjing 210097, China
    e-mail

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