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Existence results for a class of local and nonlocal nonlinear elliptic problems

Author
Temghart, Said Ait

Allalou, Chakir

Abbassi, Adil

Full text
https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3321
10.56754/0719-0646.2501.001
Abstract
In this paper, we study the \(p\)-Laplacian problems in the case where \(p\) depends on the solution itself. We consider two situations, when \(p\) is a local and nonlocal quantity. By using a singular perturbation technique, we prove the existence of weak solutions for the problem associated to the following equation \[\begin{cases}-\mathrm{d}\mathrm{i}\mathrm{v}(|\nabla u|^{p(u)-2}\nabla u)+|u|^{p(u)-2}u=f&\mbox{in}\; \Omega\\u=0& \mbox{on}\; \partial\Omega,\end{cases}\] and also for its nonlocal version. The main goal of this paper is to extend the results established by M. Chipot and H. B. de Oliveira (Math. Ann., 2019, 375, 283-306).
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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