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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 197219, 4 pages
http://dx.doi.org/10.1155/2013/197219
Research Article

A Variational Approach to an Inhomogeneous Second-Order Ordinary Differential System

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Received 26 January 2013; Accepted 4 April 2013

Academic Editor: Teoman Özer

Copyright © 2013 B. Muatjetjeja and C. M. Khalique. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the coupled inhomogeneous Lane-Emden system from the Lagrangian formulation point of view. The existence of multiple positive solutions has been discussed in the literature. Here we aim to classify the system with respect to a first-order Lagrangian according to the Noether point symmetries it admits. We then obtain first integrals of the various cases which admit Noether point symmetries.