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

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 pp-Laplace elliptic and pseudo-pp-Laplace problems.