Multiple periodic solutions for dynamic Li\'enard equations with delay and singular $\varphi$-laplacian of relativistic type

AMSTER, PABLO; KUNA, MARIEL PAULA; SANTOS, DIONICIO PASTOR

Evento Virtual, Buenos Aires

Congreso; Mathematical Congress of the Americas; 2021

In this work, we study the existence and multiplicity of $T$-periodic solutions $x:\mathbb{T} \rightarrow \mathbb{R}$ to the following equation with delay on time scales\begin{equation}\label{eq1}(\varphi(x^{\Delta}(t)))^{\Delta} +h(x(t))x^{\Delta}(t)+ g(x(t-r)) =p(t) \ \ \ t\in \mathbb{T},\end{equation}where ${\mathbb{T}}$ is an arbitrary $T$-periodic nonempty closed subset of $\mathbb{R}$ (\textit{time scale}), $\varphi:(-a,a)\rightarrow \mathbb{R}$ is anincreasing homeomorphism with $0