Date of Award:
5-2004
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Committee Chair(s)
Zhi-Qiang Wang
Committee
Zhi-Qiang Wang
Abstract
We studied some semilinear elliptic equations on the entire space R^N. Our approach was variational, and the major obstacle was the breakdown in compactness due to the unboundedness of the domain. First, we considered an asymptotically linear Scltrodinger equation under the presence of a steep potential well. Using Lusternik-Schnirelmann theory, we obtained multiple solutions depending on the interplay between the linear, and nonlinear parts. We also exploited the nodal structure of the solutions. For periodic potentials, we constructed infinitely many homoclinic-type multibump solutions. This recovers the analogues result for the superlinear case. Finally, we introduced weights on the linear and nonlinear parts, and studied how their interact ion affects the local and global compactness of the problem. Our approach is based on the Caffarelli-Kohn-Nirenberg inequalities.
Checksum
e8926de54d9588cdb63726273c98d87d
Recommended Citation
van Heerden, Francois A., "Semilinear Elliptic Equations in Unbounded Domains" (2004). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7146.
https://digitalcommons.usu.edu/etd/7146
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