Multiplicity of solutions for fractional-order differential equations via the k(x)-Laplacian operator and the genus theory
Date
2022
Authors
Srivastava, H.M.
da Costa Sousa, Jose Vanterler
Journal Title
Journal ISSN
Volume Title
Publisher
Fractal and Fractional
Abstract
In this paper, we investigate the existence and multiplicity of solutions for a class of
quasi-linear problems involving fractional differential equations in the x-fractional space (H y,β;x k(x)) (△).
Using the Genus Theory, the Concentration-Compactness Principle, and the Mountain Pass Theorem,
we show that under certain suitable assumptions the considered problem has at least k pairs of
non-trivial solutions.
Description
Keywords
fractional differential equations, k(x)-Laplacian, x-Hilfer fractional derivative, existence, multiplicity of solutions, genus theory, Concentration-Compactness Principle, Mountain Pass Theorem, variable exponents, variational methods
Citation
Srivastava, H. & da Costa Sousa, J. (2022). “Multiplicity of solutions for fractionalorder differential equations via the k(x)-Laplacian operator and the genus theory.” Fractal and Fractional, 6(9), 481. https://doi.org/10.3390/fractalfract6090481