Date of Award


Degree Type


Degree Name


Degree Program

Engineering and Applied Science



Major Professor

Saxton, Ralph

Second Advisor

Wei, Dongming

Third Advisor

Santanilla, Jairo

Fourth Advisor

Chin-Bing, Stan

Fifth Advisor

Hui, David


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.


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