Constant-sign and nodal solutions for a Neumann problem with \(p\)-Laplacian and equi-diffusive reaction term (Q446225)

The authors consider the problem NEWLINE\[NEWLINE -\Delta_pu=\lambda|u|^{p-2}u-f(x,u)\qquad\text{ in } \Omega, \qquad \frac{\partial u}{\partial n}=0 \quad \text{ on } \partial\Omega. NEWLINE\]NEWLINE It is established 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 \(\lambda.\) The proofs make use of sub- and super-solution techniques as well as critical point theory.