J. Nonl. Evol. Equ. Appl. 2016 (6), pp. 95-111, published on May 13, 2017:

Existence and uniqueness results for nonlinear anisotropic elliptic equations

Y. Akdim, A. Salmani

Laboratory LSI, Faculty Polydisciplinary of Taza, Sidi Mohamed Ben Abdellah University, P. O. Box 1223 Taza Gare, Morocco

Received on January 19, 2016
Accepted on August 6, 2016

Communicated by Ti-Jun Xiao

Abstract.  In this work, we shall be concerned with the existence and uniqueness of weak solutionsof anisotropic elliptic operators, Au + Σ gi(x, u, ∇u) + Σ Hi(x, ∇u) = f − Σ ∂i ki, where f belongs to Lp(Ω), ki belong to Lpi(Ω), and A is a Leray-Lions operator. The critical growth condition on gi is with respect to ∇u and no growth condition with respect to u, while the functions Hi grow as |∇u|pi-1.
Keywords:Existence, Uniqueness, Weak solutions, Truncations, A priori estimates, Non-linear operators, Anisotropic elliptic equations, Anisotropic Sobolev space..
2010 Mathematics Subject Classification:   35A02, 35A01.

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