Journal of Applied Nonlinear Dynamics
Multiplicity of Solutions for a Class of Nonlinear Fractional
Boundary Value Systems via Variational Approach
Journal of Applied Nonlinear Dynamics 11(4) (2022) 789--803 | DOI:10.5890/JAND.2022.12.002
Fares Kamache$^{1}$, Rafik Guefaifia$^{2}$, Salah
Boulaaras$^{3}$
$^{1}$ Laboratory of Mathematics, Informatics and systemes
(LAMIS), Larbi Tebessi University -Tebessa, Algeria
$^{2}$ Department of Mathematics, College of Sciences and Arts,
Al-Rass,
Qassim University, Kingdom of Saudi
Arabia
$^{3}$ Laboratory of Fundamental and Applied Mathematics of Oran
(LMFAO), University of Oran 1, Ahmed
Benbella, Algeria
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Abstract
In this work, it is proved the existence of at least three weak solutions
can be obtained for a new class of nonlinear fractional boundary value
systems by using variational methods combined with a critical point theory
due to Bonano and Marano while two examples in $%
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\mathbb{R}
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^{3}$ and $%
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\mathbb{R}
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^{4}$ are given to illustrate our main results applications.
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