STANDING WAVES OF NONLINEAR SCHRODINGER EQUATIONS WITH OPTIMAL CONDITIONS FOR POTENTIAL AND NONLINEARITY

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We consider the singularly perturbed nonlinear elliptic problem epsilon(2)Delta v - V(x)v + f(v) = 0, v > 0, lim(vertical bar x vertical bar ->infinity) v(x) = 0. Under almost optimal conditions for the potential V and the nonlinearity f, we establish the existence of single-peak solutions whose peak points converge to local minimum points of V as epsilon -> 0. Moreover, we exhibit a threshold on the condition of V at infinity between existence and nonexistence of solutions.
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2013-03
Language
English
Article Type
Article
Citation

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.12, no.2, pp.831 - 850

ISSN
1534-0392
DOI
10.3934/cpaa.2013.12.831
URI
http://hdl.handle.net/10203/102493
Appears in Collection
MA-Journal Papers(저널논문)
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