Existence of standing waves of nonlinear Schrodinger equations with potentials vanishing at infinity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Kwon, Ohsang

关键词: Standing waves;    Nonlinear Schrodinger equation;    Lyapunov-Schmidt reduction method;   

DOI  :  10.1016/j.jmaa.2011.09.050

来源: Elsevier

【 摘 要 】

For a singularly perturbed nonlinear elliptic equation epsilon(2) Delta u - V(x)u + u(p) = 0, x is an element of R(N), we prove the existence of bump solutions concentrating around positive critical points of V when nonnegative V is not identically zero for p is an element of (N/N-2, N+2/N-2) or nonnegative V satisfies lim inf(vertical bar x vertical bar ->infinity) V(x)vertical bar x vertical bar(2) log vertical bar x vertical bar > 0 p = N/N-2. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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