Solving p-Laplacian equations on complete manifolds

Abstract

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 $k,K:Mo mathbb{R}$.

Keywords

• Differential geometry
• nonlinear partial differential equations.