Constant-sign and nodal solutions for a Neumann problem with $p$-Laplacian and equi-diffusive reaction term

Abstract

The existence of both constant and sign-changing (namely, nodal) solutions to a Neumann boundary-value problem with $p$-Laplacian and reaction term depending on a positive parameter is established. Proofs make use of sub- and super-solution techniques as well as critical point theory.