We study the nonlinear Schrödinger type equation
- Δu + (λg(x) + l)u = f(u)
on the whole space R^N. 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 lxl →∞ . 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.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8161 |
| Date | 01 May 2002 |
| Creators | van Heerden, Francois A. |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
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