Periodic and almost periodic solutions of the Riccati equations with linear reflecting function

Almost periodic linear differential equations with non-separated solutions

A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes al...

Almost Periodic and Periodic Solutions of Difference Equations

I t is easy to see that for every point (y, N) in WXI there is a solution (n) of (1) that satisfies <1>(N) =y. This solution is defined and unique on some set N^nKN*» where N<» is maximal. (That is, either iV» = °o or ^ i V ^ — l) (£W.) The solution may or may not be continuable for nƒ> rc)> 0^w<iV o o(^ , / ) , be the soluti...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Mo> Bius Transformations and Periodic Solutions of Complex Riccati Equations

and we are going to determine all the possible dynamics of this type of equation. Also, we can say that generically there are two different T-periodic solutions. In this equation we emphasize the following antecedents. First, in 1975, there appeared a paper written by N. G. Lloyd [5] about complex solutions of a real Riccati equation. This study was continued in a 1984 paper by H. S. Hassan [3]...