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Quasilinear elliptic systems with nonstandard growth and weak monotonicity

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Abstract

We prove the existence of solutions for a quasilinear elliptic system

$$\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\,\sigma (x,u,Du)&{}=f(x,u,Du)\quad \text {in}\;\varOmega ,\\ u&{}=0\quad \text {on}\;\partial \varOmega . \end{array} \right. \end{aligned}$$

The results are obtained in Orlicz–Sobolev spaces by means of the Young measures.

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Acknowledgements

The authors would like to thank the referees for constructive suggestions which help us in depth to improve the quality of the paper.

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  1. Department of Mathematics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Atlas, Fez, Morocco

    Elhoussine Azroul & Farah Balaadich

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  1. Elhoussine Azroul
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  2. Farah Balaadich
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Correspondence to Farah Balaadich.

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Azroul, E., Balaadich, F. Quasilinear elliptic systems with nonstandard growth and weak monotonicity. Ricerche mat 69, 35–51 (2020). https://doi.org/10.1007/s11587-019-00447-x

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