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A Strongly Nonlinear Elliptic Problem with Generalized Growth in Musielak Spaces

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Abstract

In this article, we prove an existence theorem of renormalized solutions for nonlinear elliptic problem of the type

$$\begin{aligned} -\mathop {\mathrm{div}}\>{\mathcal {A}}(x,u,\nabla u)-\mathop {\mathrm{div}}\varPhi (x,u)+{\mathcal {H}}(x,u,\nabla u)= f \quad \hbox {in }{\varOmega }, \end{aligned}$$

where the first lower-order term \(\varPhi \) satisfies only a generalized natural growth condition without any supplementary assumptions. The approach does not require any particular type of growth condition on \(\varPhi \).

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Authors and Affiliations

  1. Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, Fez-Atlas, PB 1796, Fez, Morocco

    Mohamed Bourahma, Abdelmoujib Benkirane & Jaouad Bennouna

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  1. Mohamed Bourahma
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  2. Abdelmoujib Benkirane
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  3. Jaouad Bennouna
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Correspondence to Mohamed Bourahma.

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Bourahma, M., Benkirane, A. & Bennouna, J. A Strongly Nonlinear Elliptic Problem with Generalized Growth in Musielak Spaces. Differ Equ Dyn Syst 32, 51–85 (2024). https://doi.org/10.1007/s12591-020-00558-0

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