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# On positive solutions for a class of strongly coupled p-Laplacian systems

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Author(s): Jaffar Ali | R. Shivaji

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: Conference;
Issue: 16;
Start page: 29;
Date: 2007;
Original page

Keywords: Positive solutions | p-Laplacian systems | semipositone problems.

ABSTRACT
Consider the system \$\$displaylines{ -Delta_pu =lambda f(u,v)quadhbox{in }Omegacr -Delta_qv =lambda g(u,v)quadhbox{in }Omegacr u=0=v quad hbox{on }partialOmega }\$\$ where \$Delta_sz=hbox{m div}(| abla z|^{s-2} abla z)\$, \$s>1\$, \$lambda\$ is a non-negative parameter, and \$Omega\$ is a bounded domain in \$mathbb{R}\$ with smooth boundary \$partialOmega\$. We discuss the existence of a large positive solution for \$lambda\$ large when \$\$ lim_{xoinfty}frac{f(x,M[g(x,x)]^{1/q-1})}{x^{p-1}}=0 \$\$ for every \$M>0\$, and \$lim_{xoinfty} g(x,x)/x^{q-1}=0\$. In particular, we do not assume any sign conditions on \$f(0,0)\$ or \$g(0,0)\$. We also discuss a multiplicity results when \$f(0,0)=0=g(0,0)\$.

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