On positive solutions for classes of p-Laplacian semipositone systems

• DOI: 10.3934/dcds.2003.9.1063
• Publication Date: 2008-12-30T15:51:35Z
• Authors: Maya Chhetri; ; D. D. Hai; R. Shivaji
• Keywords: Nabla symbol; Center (category theory); Annulus (botany)

We study positive solutions for the system <p align="center"> $-\Delta_p u = \lambda f(v)$ in $\quad \Omega $ align="left" class="times"> v g(u)$ \quad $u 0 v$ on \partial \Omega$ where > is a parameter, \Delta_p denotes p-Laplacian operator defined by \Delta_p(z)$:=div$(|\nabla z|^{p-2}\nabla z) p> 1 and bounded domain with smooth boundary. Here f,g \in C[0,\infty) belong to class of functions satisfying \lim_{z \to \infty}\frac{f(z)}{z^{p-1}}=0, \infty}\frac{g(z)}{z^{p-1}}=0 $. In particular, we discuss existence radial large when an annulus. For general region \Omega, also non-existence result f(0) < g(0) 0.