Electron. J. Diff. Equ., Vol. 2014 (2014), No. 32, pp. 1-12.

Existence of solutions to quasilinear elliptic problems with nonlinearity and absorption-reaction gradient term

Sofiane El-Hadi Miri

Abstract:
In this article we study the quasilinear elliptic problem
$$\displaylines{
 -\Delta_p u  =  \pm |\nabla u|^\nu+f(x,u), \quad \text{in } \Omega, \cr
 u  \ge  0  \quad  \text{in }\Omega , \cr
 u  =  0  \quad \text{on  }\partial\Omega ,
 }$$
where $\Omega \subset \mathbb{R}^N$ is a bounded regular domain, p>1 and $0<\nu\le p$. Moreover, f is a nonnegative function verifying suitable hypotheses. The main goal of this work is to analyze the interaction between the gradient term and the function f to obtain existence results.

Submitted January 14, 2013. Published Janaury 27, 2014.
Math Subject Classifications: 35D05, 35D10, 35J25, 35J70, 46E30, 46E35.
Key Words: Quasi-linear elliptic problems; entropy solution; general growth

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Sofiane El-Hadi Miri
Université de Tlemcen, Faculté de Technologie
BP 230, Tlemcen 13000, Algérie.
Laboratoire d'Analyse Non-Linéaire et Mathématiques Appliquées,
Université de Tlemcen, BP 119. Tlemcen, Algérie
email: mirisofiane@yahoo.fr

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