Nonlinear versions of Stampacchia and Lax-Milgram theorems and applications to p-Laplace equations

Abstract

Abstract We obtain the nonlinear versions of the Stampacchia theorem and the Lax-Milgram theorem. Our results are stronger than the classical ones even in the linear case. Applying these theorems we get nontrivial solutions of p-Laplace elliptic and pseudo-pLaplace problems