Higher Order Analysis on the Existence of Periodic Solutions in Continuous Differential Equations via Degree Theory

On Periodic Solutions of Higher-Order Functional Differential Equations

I. Kiguradze,1 N. Partsvania,1 and B. Půža2 1 Andrea Razmadze Mathematical Institute, 1 Aleksidze Street, 0193 Tbilisi, Georgia 2Department of Mathematics and Statistics, Masaryk University, Janáčkovo nám. 2a, 66295 Brno, Czech Republic Correspondence should be addressed to I. Kiguradze, [email protected] Received 8 September 2007; Accepted 23 January 2008 Recommended by Donal O’Regan For higher...

Existence of Periodic Solutions for Higher-order Nonlinear Difference Equations

In this article, we study a higher-order nonlinear difference equation. By using critical point theory, we establish sufficient conditions for the existence of periodic solutions.

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS