Abstract
With only the log-Hölder continuity on the modular function, we prove in non-reflexive Musielak spaces an existence result of solutions for a strongly nonlinear obstacle problem associated to the elliptic equation
where the lower order term \(\Phi\) is a non-coercive Carathéodory function satisfying a generalized natural growth condition described by the appropriate Musielak function \(\varphi\) and f is an integrable datum. We do not assume any growth restrictions neither on \(\varphi\) nor on its complementary \({\overline{\varphi }}\).
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Bourahma, M., Bennouna, J. & Benkirane, A. On some nonlinear obstacle problems with only the log-Hölder continuity in Musielak spaces. São Paulo J. Math. Sci. 17, 1098–1124 (2023). https://doi.org/10.1007/s40863-022-00346-4
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DOI: https://doi.org/10.1007/s40863-022-00346-4