Multiplicity of Periodic Solutions for Dynamic Li\'enard Equations with Delay and Singular $\varphi$-laplacian of Relativistic Type

TL;DR

This paper investigates the existence and multiplicity of periodic solutions in delayed singular $\

Contribution

It introduces new topological methods to establish multiple solutions for delayed singular $\

Findings

Multiple periodic solutions are proven to exist.

The methods apply to relativistic forced pendulum equations.

The approach extends to equations on time scales.

Abstract

We study the existence and multiplicity of periodic solutions for singular $\varphi$-laplacian equations with delay on time scales. We prove the existence of multiple solutions using topological methods based on the Leray-Schauder degree. A special case is the $T$-periodic problem for the forced pendulum equation with relativistic effects.