The existence of two nontrivial solutions via homological local linking for the non-coercive p-Laplacian Neumann problem

In this paper we consider a nonlinear Neumann problem driven by the pp-Laplacian and with a Carathéodory right hand side nonlinearity f(z,x)f(z,x). The hypothesis on f(z,x)f(z,x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions.