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2021 Existence of Solutions for a Class of Fractional Kirchhoff-type Systems in $\mathbb{R}^N$ with Non-standard Growth
Elhoussine Azroul, Athmane Boumazourh, Nguyen Thanh Chung
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Taiwanese J. Math. Advance Publication 1-26 (2021). DOI: 10.11650/tjm/210503

Abstract

This paper is concerned with the existence and multiplicity of nontrivial solutions for a class of Kirchhoff-type systems in $\mathbb{R}^N$ involving the fractional pseudo-differential operators defined as the generalizations of the $p(x)$-Laplace operator. Our main tools come from a direct variational methods, the Mountain Pass Theorem, the symmetric Mountain Pass Theorem and the Fountain Theorem in critical point theory. The obtained results of this note significantly contribute to the study of Kirchhoff-type systems in the sense that our situation covers not only differential operators of fractional order but also nonhomogeneous differential operators in Sobolev spaces with variable exponent.

Acknowledgments

The authors would like to thank the anonymous referee who provided useful and detailed comments on this manuscript.

Citation

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Elhoussine Azroul. Athmane Boumazourh. Nguyen Thanh Chung. "Existence of Solutions for a Class of Fractional Kirchhoff-type Systems in $\mathbb{R}^N$ with Non-standard Growth." Taiwanese J. Math. Advance Publication 1 - 26, 2021. https://doi.org/10.11650/tjm/210503

Information

Published: 2021
First available in Project Euclid: 2 June 2021

Digital Object Identifier: 10.11650/tjm/210503

Subjects:
Primary: 35J48
Secondary: 35J50, 35R11

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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