Periodic solutions of the third order functional differential equations

Periodic solutions of first order functional differential equations

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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 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...

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

Liouvillian solutions of third order differential equations

The Kovacic algorithm and its improvements give explicit formulae for the Liouvillian solutions of second order linear differential equations. Algorithms for third order differential equations also exist, but the tools they use are more sophisticated and the computations more involved. In this paper we refine parts of the algorithm to find Liouvillian solutions of third order equations. We show...