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ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA

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Abstract

This work is devoted to studying the quasilinear elliptic system

$$\begin{aligned} -div ~ a(x,u,Du) + \vert u\vert ^{p-2} u +b(x,u,Du)=v(x)+f(x,u)+div ~g(x,u) \end{aligned}$$

on a bounded open domain of \(\mathbb {R}^n\) with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for a, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.

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Acknowledgements

The authors would like to thank the referees for the useful comments and suggestions that substantially helped improved the quality of the paper.

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  1. Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Hasnae El Hammar, Chakir Allalou & Said Melliani

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  1. Hasnae El Hammar
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  2. Chakir Allalou
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  3. Said Melliani
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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to Hasnae El Hammar.

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Hammar, H.E., Allalou, C. & Melliani, S. ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA. J Math Sci 266, 576–592 (2022). https://doi.org/10.1007/s10958-022-05951-4

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  • DOI: https://doi.org/10.1007/s10958-022-05951-4

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