Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials

This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by co...

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Bibliographic Details
Published in:Fractal and Fractional
Main Authors: Jiabin Zuo, Zakaria El Allali, Said Taarabti
Format: Article
Language:English
Published: MDPI AG 2022-10-01
Subjects:
nontrivial solutions
fourth-order
mountain pass lemma
existence
Online Access:https://www.mdpi.com/2504-3110/6/10/568
Description
Summary:This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by considering two cases. Our results not only make previous results more general but also show new insights into fourth-order elliptic problems.
ISSN:2504-3110

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