Date of Award:

5-2002

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Advisor/Chair:

Zhi-Qiang Wang

Abstract

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.

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