Nonlinear Neumann problems driven by a nonhomogeneous differential   operator
  We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator $\operatorname{div}(a(x,\nabla u))$, 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. 
Giovanni Molica Bisci and Du\v{s}an Repov\v{s}
math.AP