Nonlinear versions of Stampacchia and Lax–Milgram theorems and applications to image-Laplace equations Original Research Article

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.