Combined effects in nonlinear elliptic equations involving fractional operators

In this paper, we use variational tools in order to study the existence and the multiplicity of solutions for a nonlinear elliptic problem involving fractional operators. Precisely, we use the Mountain pass theorem to prove the existence of a nontrivial solution. Also, by combining this with the Eke...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2023-09, Vol.14 (3), Article 35
Main Authors: Chammem, Rym, Ghanmi, Abdeljabbar, Mechergui, Mahfoudh
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Elliptic functions
Existence theorems
Functional Analysis
Mathematics
Mathematics and Statistics
Mountains
Operator Theory
Operators (mathematics)
Partial Differential Equations
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Summary:In this paper, we use variational tools in order to study the existence and the multiplicity of solutions for a nonlinear elliptic problem involving fractional operators. Precisely, we use the Mountain pass theorem to prove the existence of a nontrivial solution. Also, by combining this with the Ekeland variational principle the existence of multiple solutions is proved. Moreover, the existence of infinitely many solutions is given by using the Z 2 -symmetric version for even functionals of the Mountain pass Theorem. To illustrate the usefulness of the main results an illustrative example is presented.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-023-00530-w