Lasota–Opial type conditions for periodic problem for systems of higher-order functional differential equations

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

POSITIVE PERIODIC SOLUTIONS FOR HIGHER-ORDER FUNCTIONAL q-DIFFERENCE EQUATIONS

In this paper, using the recently introduced concept of periodic functions in quantum calculus, we study the existence of positive periodic solutions of a certain higher-order functional q-difference equation. Just as for the well-known continuous and discrete versions, we use a fixed point theorem in a cone in order to establish the existence of a positive periodic solution. This paper is dedi...

Positive periodic solutions for higher order functional difference equations

In this paper, we apply a fixed point theorem to obtain sufficient conditions for the existence of positive periodic solutions for two classes of higher-order functional difference equations. AMS subject classification: 39A10.

Periodic Boundary Value Problems for Second-Order Functional Differential Equations

Upper and lower solution method plays an important role in studying boundary value problems for nonlinear differential equations; see 1 and the references therein. Recently, many authors are devoted to extend its applications to boundary value problems of functional differential equations 2–5 . Suppose α is one upper solution or lower solution of periodic boundary value problems for second-orde...