- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 197219, 4 pages
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.
- H. Zou, “A priori estimates for a semilinear elliptic system without variational structure and their applications,” Mathematische Annalen, vol. 323, no. 4, pp. 713–735, 2002.
- D. Qiuyi, “Entire positive solutions for inhomogeneous semilinear elliptic systems,” Glasgow Mathematical Journal, vol. 47, no. 1, pp. 97–114, 2005.
- P. Clément, D. G. de Figueiredo, and E. Mitidieri, “Positive solutions of semilinear elliptic systems,” Communications in Partial Differential Equations, vol. 17, no. 5-6, pp. 923–940, 1992.
- C. Cosner, “Positive solutions for superlinear elliptic systems without variational structure,” Nonlinear Analysis: Theory, Methods & Applications, vol. 8, no. 12, pp. 1427–1436, 1984.
- D. G. de Figueiredo and P. L. Felmer, “A Liouville-type theorem for elliptic systems,” Annali della Scuola Normale Superiore di Pisa, vol. 21, no. 3, pp. 387–397, 1994.
- E. Mitidieri, “A Rellich type identity and applications,” Communications in Partial Differential Equations, vol. 18, no. 1-2, pp. 125–151, 1993.
- E. Mitidieri, “Non-existence of positive solutions of semilinear elliptic systems in Rn,” Differential and Integral Equations, vol. 9, pp. 456–479, 1996.
- L. A. Peletier and R. C. A. M. van der Vorst, “Existence and nonexistence of positive solutions of nonlinear elliptic systems and the biharmonic equation,” Differential and Integral Equations, vol. 5, no. 4, pp. 747–767, 1992.
- W. Reichel and H. Zou, “Non-existence results for semilinear cooperative elliptic systems via moving spheres,” Journal of Differential Equations, vol. 161, no. 1, pp. 219–243, 2000.
- R. C. A. M. van der Vorst, “Variational identities and applications to differential systems,” Archive for Rational Mechanics and Analysis, vol. 116, no. 4, pp. 375–398, 1992.
- P. Han and Z. Liu, “Multiple positive solutions of strongly indefinite systems with critical Sobolev exponents and data that change sign,” Nonlinear Analysis: Theory, Methods & Applications, vol. 58, no. 1-2, pp. 229–243, 2004.
- D. Qiuyi and C. C. Tisdell, “Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications,” Acta Mathematica Scientia B, vol. 29, no. 2, pp. 435–446, 2009.
- H. Goldstein, C. Poole, and J. Safko, Classical Mechanics, Pearson Education, Singapore, 3rd edition, 2004.
- V. M. Gorringe and P. G. L. Leach, “Lie point symmetries for systems of second order linear ordinary differential equations,” Quaestiones Mathematicae, vol. 11, no. 1, pp. 95–117, 1988.
- B. Muatjetjeja and C. M. Khalique, “First integrals for a generalized coupled Lane-Emden system,” Nonlinear Analysis: Real World Applications, vol. 12, no. 2, pp. 1202–1212, 2011.
- B. van Brunt, The Calculus of Variations, Universitext, Springer, New York, NY, USA, 2004.
- E. Noether, “Invariante Variationsprobleme, Königliche Gesellschaft der Wissenschaften Zu Göttingen, Nachrichten,” Mathematisch-Physikalische Klasse Heft, vol. 2, pp. 235–269, 1918.