Date of Award
12-2008
Degree Type
Dissertation
Degree Name
Ph.D.
Degree Program
Engineering and Applied Science
Department
Mathematics
Major Professor
Saxton, Ralph
Second Advisor
Wei, Dongming
Third Advisor
Santanilla, Jairo
Fourth Advisor
Chin-Bing, Stan
Fifth Advisor
Hui, David
Abstract
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.
Recommended Citation
Khanfar, Abeer, "Multiple Solutions on a Ball for a Generalized Lane Emden Equation" (2008). University of New Orleans Theses and Dissertations. 901.
https://scholarworks.uno.edu/td/901
Rights
The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.