Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 111, pp. 1-16.

Title: Multiplicity of positive solutions for  quasilinear  elliptic
       p-Laplacian systems
  
Authors: Asadollah Aghajani (Iran Univ. of Science and Tech., Tehran, Iran)
         Jamileh  Shamshiri (Islamic Azad Univ., Karaj, Iran)

Abstract:
 We study the existence and multiplicity of solutions to
 the elliptic system
 $$\displaylines{
 -\hbox{div}(|\nabla u|^{p-2} \nabla u)+m_1(x)|u|^{p-2}u
 =\lambda g(x,u) \quad x\in \Omega,\cr
 -\hbox{div}(|\nabla v|^{p-2} \nabla v)+m_2(x)|v|^{p-2}v=\mu
 h(x,v)  \quad x\in \Omega,\cr
 |\nabla u|^{p-2}\frac{\partial u}{\partial n}=f_u(x,u,v),\quad
 |\nabla v|^{p-2}\frac{\partial v}{\partial n}=f_v(x,u,v),
 }$$
 where $\Omega\subset \mathbb{{R}}^N$ is
 a bounded and smooth domain.
 Using  fibering maps and  extracting Palais-Smale sequences in the
 Nehari manifold, we prove the existence of at least two
 distinct nontrivial nonnegative solutions.

Submitted June 19, 2012. Published July 02, 2012.
Math Subject Classifications: 35B38,  34B15, 35J92.
Key Words: Critical points; nonlinear boundary value problems;
    quasilinear p-Laplacian problem; fibering map; Nehari manifold.