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Existence of Solution for Nonlocal Heterogeneous Elliptic Problems

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Abstract

We consider a class of a nonlocal heterogeneous elliptic problem of type

$$\begin{aligned} -M(|u|_{q}^{q})\,div(a(x)\nabla u)=g(x,u) \end{aligned}$$

with a homogeneous Dirichlet boundary condition. Under different assumptions on the function g, we establish two existence theorems for this problem by using, respectively, the Schauder and Tychonoff fixed point theorems. Also, we give an example for each theorem.

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Authors and Affiliations

  1. Department of Mathematics, Ecole Normale Supérieure, 16050, Kouba, Algiers, Algeria

    Mahmoud Bousselsal

  2. Department of Mathematics, University of El Oued, B. P. 789, El Oued, 39000, Algeria

    Elmehdi Zaouche

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  1. Mahmoud Bousselsal
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  2. Elmehdi Zaouche
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Correspondence to Elmehdi Zaouche.

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Bousselsal, M., Zaouche, E. Existence of Solution for Nonlocal Heterogeneous Elliptic Problems. Mediterr. J. Math. 17, 129 (2020). https://doi.org/10.1007/s00009-020-01564-w

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  • DOI: https://doi.org/10.1007/s00009-020-01564-w

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