The antimaximum principle and the existence of a solution for the generalized p-Laplace equations with indefinite weight

Abstract

This paper treats the antimaximum principle and the existence of a solution for quasi- linear elliptic equation −div (a(x,|∇u|)∇u )= λm(x)|u| p−2 u+h(x) in Ω under the Neumann boundary condition. Here, a map a(x,|y|)y on Ω ×R N is strictly monotone in the second vari- able and satisfies certain regularity conditions. This equation contains the p-Laplacian problem as a special case.