### 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.

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.

#### Keywords

p-Laplacian; Neumann problem; constant-sign solutions; nodal solutions; truncations; sub- and super-solutions; critical groups

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