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Existence results for some nonlinear elliptic equations via topological degree methods

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Abstract

This article is devoted to study the existence of weak solutions to a Dirichlet boundary value problem related to the following nonlinear elliptic equation

$$\begin{aligned} -div\left( a(x,u,\nabla u)\right) -\lambda g(x,u,\nabla u)=b(x)|u|^{q-2}u, \end{aligned}$$

where \(-div\left( a(x,u,\nabla u)\right) \) is a Leray-Lions operator acting from \(W_0^{1,p}(\varOmega ,w)\) to its dual \(W^{-1,p'}(\varOmega ,w^*)\). On the nonlinear term \(g(x,s,\eta )\), we only assume the growth condition on \(\eta \). Our approach is based on the topological degree introduced by Berkovits.

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Authors and Affiliations

  1. Laboratory LMACS, FST of Beni Mellal, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Adil Abbassi, Chakir Allalou & Abderrazak Kassidi

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  1. Adil Abbassi
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  2. Chakir Allalou
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  3. Abderrazak Kassidi
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Correspondence to Abderrazak Kassidi.

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Abbassi, A., Allalou, C. & Kassidi, A. Existence results for some nonlinear elliptic equations via topological degree methods. J Elliptic Parabol Equ 7, 121–136 (2021). https://doi.org/10.1007/s41808-021-00098-w

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  • DOI: https://doi.org/10.1007/s41808-021-00098-w

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