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Anisotropic equations in weighted Sobolev spaces of higher order

Authors:

Institution:

(1) Department of Mathematics and Informatics, Faculty of Sciences, DM, Université Sidi Mohamed Ben Abde lah, B.P. 1796, Atlas-Fès, Fès, 30000, Morocco;(2) Department of Mathematics, Faculty of Sciences, Al-Imam University, P.O. Box 90950, Riyadh, 11623, Saudi Arabia

Abstract:

We consider the strongly nonlinear boundary value problem,

where A is an elliptic operator of finite or infinite order. We introduce anisotropic weighted Sobolev spaces and we show under a certain sign condition of the Carathéodory function g without assuming any growth restrictions, the existence of the weak solutions.

Keywords:

Anisotropic weighted Sobolev spaces Higher order Finite and infinite orders Monotonicity condition Sign condition Existence results

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