Radial Solutions to an Elliptic Boundary Valued Problem

The author grants HarveyMudd College the nonexclusive right to make this work available for noncommercial, educational purposes, provided that this copyright statement appears on the reproduced materials and notice is given that the copy-ing is by permission of the author. To disseminate otherwise or to republish re-quires written permission from the author. In this paper we prove that{ div(|x|β∇u) + |x|α f (u) = 0, in B u = 0 on ∂B has infinitely many solutions when f is superlinear and grows subcritically for u ≥ 0 and up to critically for u less than 0 with 1 < p < N+2α−β+2N+β−2, N + α> 0, 1 < q ≤ N+2α−β+2N+β−2, α < β < α+ 1, N> 3 We make extensive use of Pohozaev identities and phase plane and energy arguments. Acknowledgments I would like to thank Professor Alfonso Castro for his guidance and support throughout the entire thesis process. I would also like to thank Professor Andrew Bernoff for giving me advice to better my presentations on the thesis and Professor Jon Jacobsen for being my second reader. Also I would like to thank my parents for their unconditional support. Additionally I would like to thank the Harvey Mudd math department for knowledge and resources they providedme throughout this process. Finally thank you Claire Connelly for making the class files and printing posters that made my thesis experience so much easier