2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 83-94.

On a problem of lower limit in the study of nonresonance with Leray-Lions operator

Aomar Anane, Omar Chakrone, Mohammed Chehabi

Abstract:
We prove the solvability of the Dirichlet problem
$$\displaylines{ Au = f(u)+h \quad\text{in } \Omega , \cr u = 0 \quad\text{on }\partial \Omega }$$
for a given $h$, under a condition involving only the asymptotic behaviour of the potential $F$ of $f$, where $A$ is a Leray-Lions operator.

Published September 20, 2006.
Math Subject Classifications: 35J60, 35P30.
Key Words: Leray-Lions operator; Nonresonance; fist eigenvalue.

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Aomar Anane
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: anane@sciences.univ-oujda.ac.ma
Omar Chakrone
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: chakrone@sciences.univ-oujda.ac.ma
Mohammed Chehabi
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: chehb_md@yahoo.fr

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