What are the roles of two competing potential functions $V(x)$ and $K(x)$ in the process of concentration for ground state solutions of an elliptic equation $h\sp2\Delta u-V(x)u+ K(x)\vert u\vert\sp{p-1}u=0,x\in R\sp{n}$ arising in the study of standing wave solutions to nonlinear Schrodinger equations? This is the motivating question and one of the questions this dissertation answers. After a careful analysis of movement of the energy, the existence and concentration behaviors of ground states are established and an explicit formula for the concentration points are found. Then the variational methods are adapted to attack an equation with more general nonlinear terms. Similar results are obtained and two limiting situations are discussed On another direction, it is proved that positive bound states for nonlinear Schrodinger equations exist and these solutions can form sequences concentrating at each critical point of a so-called minimax value function under certain technical conditions. At the end, a necessary condition for concentration of positive bound states is given / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_27053 |
| Date | January 1995 |
| Contributors | Zeng, Bin (Author), Wang, Xuefeng (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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