Abstract
In this work we are interested in the periodic solutions of the singular problem involving variable exponent with a homogeneous Dirichlet boundary conditions modeled as
Where \(\varOmega \) is an open regular bounded subset of \({\mathbb {R}}^{N}\), \(T>0\) is the period, \(\gamma (t,x)\) is a nonnegative periodic function belonging in \({\mathcal {C}}(\overline{Q_{T}})\) and f is a nonnegative measurable function periodic in time with period T and belonging to a certain Lebesgue space. Under suitable assumptions on \(\gamma \) and f, we prove an existence result of a nonnegative weak time periodic solution to the considered problem.
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The authors would like to express their sincere gratitude to the anonymous referees and the handling editor for their careful reading of the manuscript and their valuable comments, remarks and suggestions that have improved the writing of our paper in several points.
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Charkaoui, A., Taourirte, L. & Alaa, N.E. Periodic parabolic equation involving singular nonlinearity with variable exponent. Ricerche mat 72, 973–989 (2023). https://doi.org/10.1007/s11587-021-00609-w
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DOI: https://doi.org/10.1007/s11587-021-00609-w