Khafagy, Salah A.; Serag, Hassan M. Maximum principle and existence of positive solutions for nonlinear systems involving degenerate \(p\)-Laplacian operators. (English) Zbl 1137.35322 Electron. J. Differ. Equ. 2007, Paper No. 66, 14 p. (2007). Summary: We study the maximum principle and existence of positive solutions for the nonlinear system \[ \begin{aligned} -\Delta _{p,_{P}}u&= a(x)|u|^{p-2}u+b(x)|u|^{\alpha }|v|^{\beta }v+f \quad \text{in } \Omega , \\ -\Delta _{Q,q}v&= c(x)|u|^{\alpha }|v|^{\beta }u+d(x)|v|^{q-2}v+g \quad \text{in } \Omega , \\ u&=v=0 \quad \text{on }\partial \Omega , \end{aligned} \] where the degenerate \(p\)-Laplacian defined as \(\Delta _{p,_{P}}u=\text{div}[P(x)|\nabla u|^{p-2}\nabla u]\). We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method. Cited in 1 Document MSC: 35B50 Maximum principles in context of PDEs 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35J55 Systems of elliptic equations, boundary value problems (MSC2000) Keywords:degenerated \(p\)-Laplacian PDFBibTeX XMLCite \textit{S. A. Khafagy} and \textit{H. M. Serag}, Electron. J. Differ. Equ. 2007, Paper No. 66, 14 p. (2007; Zbl 1137.35322) Full Text: EuDML EMIS