Date of Award:
5-2002
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Zhi-Qiang Wang
Committee
Zhi-Qiang Wang
Committee
L. Littlejohn
Committee
X. Ren
Committee
J. Koebbe
Abstract
We study the nonlinear Schrödinger type equation
–Δu + (λg(x) + 1)u = f(u)
on the whole space RN. The nonlinearity f is assumed to be asymptotically linear and g(x) ≥ 0 has a potential well. We do not assume a limit for g(x) as |x| → ∞ . Using variational techniques, we prove the existence of a positive solution for λ large. In the case where f is odd we obtain multiple pairs of solutions. The limiting behavior of solutions as λ → ∞ is also considered.
Checksum
01f5cc37730128a02d741b06173da6f3
Recommended Citation
van Heerden, Francois A., "Nonlinear Schrödinger Type Equations with Asymptotically Linear Terms" (2002). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7089.
https://digitalcommons.usu.edu/etd/7089
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