DOI: 10.24193/fpt-ro.2026.2.11

Authors: Yan Qiao, Fangqi Chen

Abstract: We discuss a class of fractional \(p\)-Laplacian boundary value problem with a parameter on time scales. The novelty of this paper is that the existence of infinitely many solutions of the equation is obtained by using the genus property of critical point theory under the condition of weaker than the super \(p\) times Ambrosetti-Rabinowitz condition. What’s more, the existence of infinitely many solutions is proved via the symmetric mountain pass theorem with the Ambrosetti-Rabinowitz condition. At the end, an example is presented to illustrate our main results.

Key Words and Phrases: Fractional boundary value problem, \(p\)-Laplacian, time scale, critical point theorem

2020 Mathematics Subject Classification: 34A08, 34B15, 34L30, 47H10.

Published on-line: June 1st, 2026.

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