Eigenvalue analysis for the p-Laplacian under convective perturbation

In this paper a detailed analysis of the eigenvalue problem under convection −(|u′|p−2u′)′−c|u′|p−2u′=λ|u|p−2u, 0<x<1, u(0)=u(1)=0 (′=d/dx) is performed. The analysis is based on a complete study of the phase space of the family of equations (|u′|p−2u′)′+a|u′|p−2u′+b|u|p−2u=0, a,b constants.