Nonlinear Neumann problems driven by a nonhomogeneous differential operator

Abstract

We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator $\mathrm{div}(a(x,\nabla u))$, a special case of which is the $p$-Laplacian. The reaction term is a nonlinearity function $f$ which exhibits $(p-1)$-subcritical growth. By using variational methods, we prove a multiplicity result on the existence of weak solutions for such problems. An explicit example of an application is also presented.