Nontrivial solutions for a class of fractional difference boundary value problems and fixed-point problems

doi:10.3868/s140-DDD-023-0012-x

Front. Math. China

2023, Vol. 18

Issue (3) : 175-185 https://doi.org/10.3868/s140-DDD-023-0012-x

RESEARCH　ARTICLE

Nontrivial solutions for a class of fractional difference boundary value problems and fixed-point problems

Jiafa XU¹(

), Wei DONG²

¹. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
². Department of Mathematics, Hebei University of Engineering, Handan 056038, China

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Abstract

In this work, we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:

　　　　　　　　 ${T Δ t − 1 ν (t Δ ν − 1 ν x (t)) = f (x (t + ν − 1)), t ∈ [0, T] N 0, x (ν − 2) = [t Δ ν − 1 ν x (t)] t = T = 0.$

The existence of nontrivial solutions is obtained in the case of super quadratic growth of the nonlinear term $f$ by change of fountain theorem.

Keywords Fractional difference boundary value problem fountain theorem nontrivial solution

Corresponding Author(s): Jiafa XU

Online First Date: 16 November 2023 Issue Date: 07 December 2023

Cite this article:

Jiafa XU,Wei DONG. Nontrivial solutions for a class of fractional difference boundary value problems and fixed-point problems[J]. Front. Math. China, 2023, 18(3): 175-185.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0012-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I3/175

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