Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter

Abstract

A nonlinear elliptic equation with $p$-Laplacian, concave-convex reaction term depending on a parameter $\lambda>0$, and homogeneous boundary condition, is investigated. A bifurcation result, which describes the set of positive solutions as $\lambda$ varies, is obtained through variational methods combined with truncation and comparison techniques.