Existence of Solutions for a Class of p-Laplace Equations Involving Robin Boundary Value Conditions

A probe is made into the existence of a class of p-Laplace equations with Robin boundary value condition. By applying the Sobolev compact embedding theorem and assumptions given, it is proven that the energy functional of this type of equations is of a Mountain Pass type structure and satisfies the(PS)condition. Consequently, the existence of the nontrivial weak solutions of the p-Laplace equations in the Sobolev spaceW ^1,p(Ω)is obtained by the use of the Mountain Pass Lemma.