In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding.
| Identifer | oai:union.ndltd.org:uno.edu/oai:scholarworks.uno.edu:td-1882 |
| Date | 19 December 2008 |
| Creators | Khanfar, Abeer |
| Publisher | ScholarWorks@UNO |
| Source Sets | University of New Orleans |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | University of New Orleans Theses and Dissertations |
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