Existence of positive periodic solutions for delay dynamic equations

Abstract

In this article we study the existence of positive periodic solutions for a dynamic equations on time scales. The main tool employed here is the Schauder's fixed point theorem. The results obtained here extend the work of Olach [12]. Two examples are also given to illustrate this work.Subjclass [2000] : Primary 34K13, 34A34; Secondary 34K30, 34L30.

Existence and Exponential Stability of Positive Periodic Solutions for Second-Order Dynamic Equations

“…The theory of dynamic equations is a fairly new branch in mathematics (see [1][2][3][4][5][6][7][8][9][10][14][15][16][17]). Dynamic equations extend and unify the difference and differential equations.…”

“…For example, these equations appear in applied sciences, physics, chemistry, biology, medicine, etc. In particular, qualitative analysis such as positivity, periodicity and stability of solutions of dynamic equations on time scales has received the attention of many authors, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein.…”

Periodic solutions of almost linear Volterra integro-dynamic systems

“…A time scale is an arbitrary nonempty closed subset of real numbers. The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing (see [1]- [12], [16]- [19] and papers therein). The theory of dynamic equations unifies the theories of differential equations and difference equations.…”