2006 International Conference in Honor of Jacqueline Fleckinger.
Electronic Journal of Differential Equations,
Conference 16 (2007), pp. 29-34. 

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

Authors: Jaffar Ali (Mississippi State Univ., MS, USA) 
         R. Shivaji (Mississippi State Univ., MS, USA)
 
Abstract: 
 Consider the system
$$\displaylines{
 -\Delta_pu =\lambda f(u,v)\quad\hbox{in }\Omega\cr
 -\Delta_qv =\lambda g(u,v)\quad\hbox{in }\Omega\cr
  u=0=v \quad \hbox{on }\partial\Omega
}$$
 where $\Delta_sz=\hbox{\rm div}(|\nabla z|^{s-2}\nabla z)$, $s>1$,
 $\lambda$ is a non-negative parameter, and $\Omega$ is a bounded
 domain in $\mathbb{R}$ with smooth boundary $\partial\Omega$. We
 discuss the existence of a large positive solution for $\lambda$
 large when
 $$
 \lim_{x\to\infty}\frac{f(x,M[g(x,x)]^{1/q-1})}{x^{p-1}}=0
 $$
 for every $M>0$, and $\lim_{x\to\infty} g(x,x)/x^{q-1}=0$. In
 particular, we do not assume any sign conditions on $f(0,0)$ or
 $g(0,0)$. We also discuss a multiplicity results when
 $f(0,0)=0=g(0,0)$.

Published May 15, 2007.
Math Subject Classifications: 35J55, 35J70.
Key Words: Positive solutions; p-Laplacian systems; semipositone problems.