Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 34, Issue 12, Pages 1566-1591Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300903346721
Keywords
Bound states; Concentrating solutions; Critical point; Potential vanishing or unbounded at infinity; Variational method
Categories
Funding
- Natural Science Foundation of China (NSFC) [10631030, 10721101]
- Program for New Century Excellent Talents in University [07-0350]
- Chinese Ministry of Education [107081]
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In this paper we study the existence and qualitative property of standing wave solutions [image omitted] for the nonlinear Schrodinger equation [image omitted]. Let [image omitted]. For any integer k epsilon 1, we prove existence of standing wave solutions with u0 having k local maximum points and concentrating near a given local maximum point of when epsilon is small. The potentials V and K are allowed to be either vanishing or unbounded at infinity. Existence of solutions concentrating near k distinct non-degenerate critical points of has been proved under the same assumptions on V and K as well.
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