Date of Award:
Master of Science (MS)
Mathematics and Statistics
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.
van Heerden, Francois A., "Nonlinear Schrödinger Type Equations with Asymptotically Linear Terms" (2002). All Graduate Theses and Dissertations. 7089.
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