Multiple Solutions for a Dynamic Sturm-Liouville Boundary Value Problem on Time Scales with Impulsive Effects

Abstract

In this study, we explore the existence of multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales that incorporate impulsive effects. Utilizing variational methods and applying certain critical point theorems from Ricceri for smooth functionals, we demonstrate the existence of at least three solutions to the problem. To illustrate the practical relevance of our findings, we provide an example at the end. © 2025 Universita di Catania. All rights reserved.