Annals of Functional Analysis

Solutions of nonlinear elliptic problems with lower order terms

Youssef Akdim, Abdelmoujib Benkirane, and Mostafa El Moumni

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We give an existence result for strongly nonlinear elliptic equations of the form \[ -{\rm div}(a(x,u,\nabla u))+g(x,u,\nabla u)+H(x,\nabla u) = \mu\ \text{in}\ \Omega, \] where the right hand side belongs to $L^1(\Omega)+W^{-1,p'}(\Omega)$ and $- {\rm div}(a(x,u,\nabla u))$ is a Leray--Lions type operator with growth $|\nabla u|^{p-1}$ in $\nabla u$. The critical growth condition on $g$ is with respect to $\nabla u$ and no growth condition with respect to $u$, while the function $H(x,\nabla u)$ grows as $|\nabla u|^{p-1}$.

Article information

Ann. Funct. Anal., Volume 6, Number 1 (2015), 34-53.

First available in Project Euclid: 19 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B45
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 35J60: Nonlinear elliptic equations

Sobolev spaces a priori estimates nonlinear elliptic equation


Akdim, Youssef; Benkirane, Abdelmoujib; El Moumni, Mostafa. Solutions of nonlinear elliptic problems with lower order terms. Ann. Funct. Anal. 6 (2015), no. 1, 34--53. doi:10.15352/afa/06-1-4.

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