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On positive solutions of quasilinear elliptic systems

Authors:	Yuanji Cheng

Institution:	(1) Department of Mathematics, Luleå University of Technology, 97187 Luleå, Sweden

Abstract:	In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems $\left\{ \begin{gathered} - \Delta _p u = f(x,u,v), in \Omega , \hfill \\ - \Delta _p u = g(x,u,v), in \Omega , \hfill \\ u = v = 0, on \partial \Omega , \hfill \\ \end{gathered} \right.$ where –_p is the p-Laplace operator, p > 1 and is a C ^1,-domain in $\mathbb{R}^n$ . We prove an analogue of 7, 16] for the eigenvalue problem with $f(x,u,v) = {\lambda }_{1} v^{p - 1} ,{ }g(x,u,v) = {\lambda }_{2} u^{p - 1}$ and obtain a non-existence result of positive solutions for the general systems.

Keywords:	Eigenvalue problem Degenerate elliptic operator Nonlinear systems Positive solutions
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