A criterion for oscillations in the solutions of the polytropic Lane-Emden equations

We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to superlinear Lane-Emden equations with integer polytropic indices n > 1...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2016; no. 1; pp. 1 - 9
Main Authors Christodoulou, Dimitris M, Katatbeh, Qutaibeh D, Graham-Eagle, James
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 04.06.2016
Springer Nature B.V
SpringerOpen
Subjects
Analysis
analytical theory
Applications of Mathematics
Computational fluid dynamics
Criteria
Differential equations
Inequalities
Lane-Emden differential equations
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
nonlinear differential equations
Oscillations
Texts
transformations
Lane-Emden differential equations
analytical theory
76N15
34A25
34A34
transformations
oscillations
nonlinear differential equations
85A30
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Summary:We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to superlinear Lane-Emden equations with integer polytropic indices n > 1 . We confirm the validity of the analytical results by solving numerically both the cylindrical and the spherical Lane-Emden equations subject to the usual astrophysical boundary conditions for self-gravitating fluids.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-016-1086-0