Periodic Solutions for Nonlinearnth Order Ordinary Differential Equations

Order Ordinary Differential Equations

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

Periodic solutions of quaternionic-valued ordinary differential equations

This paper uses topological degree methods to prove the existence of periodic solutions of some quaternionic-valued ordinary differential equations. Mathematics Subject Classification (2000). 34C25, 11R52

Existence of periodic solutions of (2n + 1)th-order ordinary differential equations

The goal of this paper is to prove the existence and uniqueness of periodic solutions for a class of the odd order differential equations. Here the Leray–Schauder degree theory and the Schwarz inequality are used.  2002 Elsevier Science (USA). All rights reserved.

Positive periodic solutions of singular systems of first order ordinary differential equations

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone. 2011 Elsevier Inc. All rights reserved.

Positive Periodic Solutions of Systems of Second Order Ordinary Differential Equations