A criterion for oscillations in the solutions of the polytropic Lane-Emden equations
Abstract 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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1086-0 |
| Summary: | Abstract 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 $n > 1$ . 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 |