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2014 Strongly Nonlinear $p(x)$-Elliptic Problems with $L^1$-Data
E. Azroul, A. Barbara, H. Hjiaj
Afr. Diaspora J. Math. (N.S.) 16(2): 1-22 (2014).

Abstract

In this paper, we will study the existence of solutions in the sense of distributions for the quasilinear $p(x)$-elliptic problem, $$ Au + g(x,u,\nabla u) = f,$$ where $A$ is a Leray-Lions operator from $W_{0}^{1,p(\cdot)}(\Omega)$ into its dual, the nonlinear term $g(x,s,\xi)$ has a growth condition with respect to $\xi$ and the sign condition with respect to $s.$ The datum $\>f\>$ is assumed in the dual space $\>W^{-1,p'(\cdot)}(\Omega),\>$ and then in $\>L^{1}(\Omega).$

Citation

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E. Azroul. A. Barbara. H. Hjiaj. "Strongly Nonlinear $p(x)$-Elliptic Problems with $L^1$-Data." Afr. Diaspora J. Math. (N.S.) 16 (2) 1 - 22, 2014.

Information

Published: 2014
First available in Project Euclid: 20 October 2014

zbMATH: 1331.35111
MathSciNet: MR3270003

Subjects:
Primary: 35J20 , 35J60

Keywords: Lebesgue and Sobolev spaces with variable exponents , solution in the sense of distributions , strongly nonlinear p(x)-elliptic problems , truncations

Rights: Copyright © 2014 Mathematical Research Publishers

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Vol.16 • No. 2 • 2014
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