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An \(L^1\)-theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients

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Abstract

We investigate the existence of a time-periodic solution to a nonlinear evolution equation involving p(x)-growth conditions with irregular data. We tackle our problem in a suitable functional setting by considering the so-called variable exponent Lebesgue and Sobolev spaces. By assuming that the data belongs only to \(L^1\), we prove the existence of a renormalized time-periodic solution to the studied model.

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Authors and Affiliations

  1. Interdisciplinary Research Laboratory in Sciences, Education and Training, Higher School of Education and Training Berrechid (ESEFB), Hassan First University, Berrechid, Morocco

    Abderrahim Charkaoui

  2. Laboratory LAMAI, Faculty of Sciences and Technology of Marrakesh, Cadi Ayyad University, Marrakech, Morocco

    Nour Eddine Alaa

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  1. Abderrahim Charkaoui
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  2. Nour Eddine Alaa
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Charkaoui, A., Alaa, N.E. An \(L^1\)-theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients. J. Evol. Equ. 23, 73 (2023). https://doi.org/10.1007/s00028-023-00924-9

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