Multiple Solutions on a Ball for a Generalized Lane Emden Equation

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2008

Author dc:creator

• Khanfar, Abeer

Contributors dc:contributor

• Saxton, Ralph
• Wei, Dongming
• Santanilla, Jairo

• p-laplacian
• critical Sobolev exponents
• weighted Sobolev spaces

Repository record dc:identifier

https://scholarworks.uno.edu/td/901

OAI identifier oai:identifier

oai:scholarworks.uno.edu:td-1882