Existence and multiplicity results for elliptic problems with Nonlinear Boundary Conditions and variable exponents

By applying the Ricceri's three critical points theorem, we show the existence of at least three solutions to the following elleptic problem: -div [a(x, del u)] + |u|(p(x)-2)u=lambda f(x, u), in Omega, a(x, del u),v = mu g(x, u), on partial derivative Omega, where lambda, mu is an element of R-| , Omega subset of R-N (N >= 2) is a bounded domain of smooth of smooth boundary partial derivative Omega and v is the outward normal vector on partial derivative Omega. p : (Omega) over bar -> R, a :<(Omega)over bar x R-N -> R-N,R- f : Omega x R -> R and g : partial derivative Omega x R -> R are fulfilling appropriate conditions .