On oscillatory behavior of two-dimensional time scale systems

Abstract

This paper deals with long-time behaviors of nonoscillatory solutions of a system of first-order dynamic equations on time scales. Some well-known fixed point theorems and double improper integrals are used to prove the main results.

Dynamical behavior of a system of three-dimensional nonlinear difference equations

“…One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathematical models that describe real life situations in population biology, economics, probability theory, genetics, psychology, and so forth, see [3,5,8,9]. Also, similar works in two and three dimensions (limit behaviors) for more general cases, i.e., continuous and discrete cases, have been done by some authors, see [1,[11][12][13]16]. There are many papers in which systems of difference equations have been studied, as in the examples given below.…”

Oscillation Criteria of Two-Dimensional Time-Scale Systems

“…This chapter is organized as follows: In Section 2, we give the calculus of the time-scale theory for those who are not familiar with the time scale (see [5]). In Section 3, referred to [25,26], we show the existence and asymptotic behaviors of nonoscillatory solutions of a two-dimensional homogeneous dynamical system on time scales by using improper integrals and some inequalities. We also give enough examples for readers to see our results work nicely.…”