On a strongly anisotropic equation with L¹ data

Abstract

In this article, we shall be concerned with the existence of solutions for the strongly non-linear boundary value problem:

where A is an elliptic operator of finite order defined from an anisotropic Sobolev space of order m to its dual, g is a Carathéodory function satisfying essentially a sign condition on u with no growth restrictions and f belongs to L ¹.

Keywords:

• strongly non-linear problem
• anisotropic spaces
• finite order
• L ¹ data
• monotonicity condition
• sign condition

Mathematics subject classifications: :

• 35J60
• 35J65
• 35J70

Acknowledgement

The research of S. El Manouni is supported by Al-Imam University project No. 28/12.