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DOI: 10.23952/jnfa.2026.13
Received December 11, 2024; Accepted January 3, 2026; Published May 8, 2026
Abstract. This study investigates the multiplicity of solutions for a system of p-Laplacian fractional differential equations (FDEs) subjected to both instantaneous and non-instantaneous impulses. By employing a variant of Bonanno’s local minimum theorem, we establish the existence of one or two solutions under appropriate algebraic conditions, including the classical Ambrosetti-Rabinowitz (AR) condition applied to the nonlinear term. Additionally, utilizing the critical point theorems proposed by Averna and Bonanno, we explore the existence of two and three solutions in a specific scenario of the system. The results contribute to a deeper understanding of the solution structure of impulsive FDEs and demonstrate the effectiveness of advanced variational techniques in addressing complex differential systems.
How to Cite this Article:
F. Ayazi, E. Ghaderi, A. Salari, S. Naseri, Multiplicity of solutions for p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses: An advanced variational method, J. Nonlinear Funct. Anal. 2026 (2026) 13.