Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 3
116
Views
6
CrossRef citations to date
0
Altmetric
Articles

A variational formulation approach to a generalized coupled inhomogeneous Emden–Fowler system

&
Pages 466-474 | Received 30 May 2012, Published online: 07 May 2013

References

  • Lane JH. On the theoretical temperature of the sun under hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment. American Journal of Science. 1869;50:57–74.
  • Emden VR. Gaskugeln Anwendungen der mechanischen Warmetheorie auf kosmologische und meteorologische Probleme. Teubner-Verlag: Leipzig; 1907.
  • Fowler RH. Further studies of Emden’s and similar differential equations. Quarterly Journal of Mathematics (Oxford Series). 1931;2:259–288.
  • Parand K, Rezaei AR, Taghavi A. Lagrangian method for solving Lane–Emden type equation arising in astrophysics on semi-infinite domains. Acta Astronautica. 2010;67:673–680.
  • Chandrasekhar S. An introduction to the study of stellar structure. New York (NY): Dover; 1957.
  • Davis HT. Introduction to nonlinear differential and integral equations. New York (NY): Dover; 1962.
  • Muatjetjeja B, Khalique CM. Exact solutions of the generalized Lane–Emden equations of the first and second kind. Pramana - Journal of Physics. 2011;77:545–554.
  • Wong JSW. On the generalized Emden–Fowler equation. SIAM Review. 1975;17:339–360.
  • Govinder KS, Leach PGL. Integrability analysis of the Emden–Fowler equation. Journal of Nonlinear Mathematical Physics. 2007;14:443–461.
  • Bidaut-Veron MF, Giacomini H. A new dynamical approach of Emden–Fowler equations and systems arXiv:1001.0562v2 [math.AP].
  • Khalique CM, Mahomed FM, Muatjetjeja B. Lagrangian formulation of a generalized Lane–Emden equation and double reduction. Journal of. Nonlinear Mathematical Physics. 2008;15:152–161.
  • Zou H. A priori estimates for a semilinear elliptic system without variational structure and their applications. Mathematische Annalen. 2002;323:713–735.
  • Qiuyi D. Entire positive solutions for inhomogeneous semilinear elliptic systems. Glasgow Mathematical Journal. 2005;47:97–114.
  • Clement Ph, de Figueiredo DG, Mitidieri E. Positive solutions of semilinear elliptic systems. Communications in Partial Differential Equations. 1992;17:923–940.
  • Cosner C. Positive solutions for superlinear elliptic systems without variational structure. Nonlinear Analysis. 1984;8:1427–1436.
  • de Figueiredo DG, Felmer P. A Liouville type theorem for systems. Annali della Scuola Normale Superiore di Pisa. 1994;21:387–397.
  • Mitidieri E. A Rellich type identity and applications. Communications in Partial Differential Equations. 1993;18:125–151.
  • Mitidieri E. Non-existence of positive solutions of semilinear elliptic systems in Rn. Differential and Integration Equations. 1996;9:456–479.
  • Peletier LA, Vorst RCAM. Existence and non-existence of positive solutions of nonlinear elliptic systems and the biharmonic equations. Differential and Integration Equations. 1992;5:747–767.
  • Reichel W, Zou H. Non-existence results for semilinear cooperative elliptic systems via moving sphere. Journal of Differential Equations. 2000;161:219–243.
  • van der Vorst RCAM. Variational identities and applications to differential systems. Archive for Rational Mechanics and Analysis. 1991;116:375–398.
  • Han P, Liu Z. Multiple positive solutions of strongly indefinite systems with critical Sobolev exponents and data that change sign. Nonlinear Analysis. 2004;58:229–243.
  • Qiuyi D, Tisdell CC. Non-degeneracy of positive solutions to homogeneous second order differential systems and its applications. Acta Mathematica Scientia. 2009;29B:435–446.
  • Bozhkov Y, Martins ACG. Lie point symmetries of the Lane-Emden systems. Journal of Mathematical Analysis and Applications. 2004;294:334–344.
  • Muatjetjeja B, Khalique CM. Noether, partial Noether operators and first integrals for the coupled Lane–Emden system. Applied Mathematics and Computation. 2010;15:325–333.
  • Muatjetjeja B, Khalique CM. Lagrangian approach to a generalized coupled Lane–Emden system: symmetries and first integrals. Communications in Nonlinear Science and Numerical Simulation. 2010;15:1166–1171.
  • Goldstein H, Poole C, Safko J. Classical mechanics. Singapore: Pearson Education; 2004.
  • Muatjetjeja B, Khalique CM. First integrals for a generalized coupled Lane–Emden systen. Nonlinear Analysis: Real World Applications. 2011;12:1202–1212.
  • Gorringe VM, Leach PGL. Lie point symmetries for systems of second order linear ordinary differential equations. Quaestiones Mathematicae. 1998;11:95–117.
  • Noether E. Invariante Variationsprobleme, König Gesell Wissen Göttingen. Math-Phys. Klasse. 1918;12:235–269.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.