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Anisotropic equations in weighted Sobolev spaces of higher order

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Abstract

We consider the strongly nonlinear boundary value problem,

$$Au+g(x,u)=f$$

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.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, DM, Université Sidi Mohamed Ben Abde lah, B.P. 1796, Atlas-Fès, Fès, 30000, Morocco

    M. Chrif

  2. Department of Mathematics, Faculty of Sciences, Al-Imam University, P.O. Box 90950, Riyadh, 11623, Saudi Arabia

    S. El Manouni

Authors
  1. M. Chrif
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  2. S. El Manouni
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Correspondence to S. El Manouni.

Additional information

Communicated by R. De Arcangelis.

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Chrif, M., El Manouni, S. Anisotropic equations in weighted Sobolev spaces of higher order. Ricerche mat. 58, 1–14 (2009). https://doi.org/10.1007/s11587-009-0045-1

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  • DOI: https://doi.org/10.1007/s11587-009-0045-1

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