Benalili, Mohammed; Maliki, Youssef Solving \(p\)-Laplacian equations on complete manifolds. (English) Zbl 1113.58014 Electron. J. Differ. Equ. 2006, Paper No. 155, 9 p. (2006). Summary: Using a reduced version of the sub and super-solutions method, we prove that the equation \(\Delta _{p}u+ku^{p-1}-Ku^{p^{\ast }-1}=0\) has a positive solution on a complete Riemannian manifold for appropriate functions \(k,K: M\to \mathbb{R}\). Cited in 7 Documents MSC: 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 31C45 Other generalizations (nonlinear potential theory, etc.) 35J60 Nonlinear elliptic equations Keywords:differential geometry; nonlinear partial differential equations PDFBibTeX XMLCite \textit{M. Benalili} and \textit{Y. Maliki}, Electron. J. Differ. Equ. 2006, Paper No. 155, 9 p. (2006; Zbl 1113.58014) Full Text: EuDML EMIS