STANDING WAVE CONCENTRATING ON COMPACT MANIFOLDS FOR NONLINEAR SCHRODINGER EQUATIONS

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For k = 1, ... , K, let M-k be a q(k)-dimensional smooth compact framed manifold in R-N with q(k) epsilon {1, ... , N - 1}. We consider the equation -epsilon(2) Delta u + V(x)u - u(p) = 0 in R-N where for each k epsilon {1, ... , K} and some m(k) > 0; V (x) = |dist(x, M-k)|(mk) + O(|dist(x, M-k)|(mk+1)) as dist( x, M-k) -> 0. For a sequence of epsilon converging to zero, we will find a positive solution u(epsilon) of the equation which concentrates on M-1 boolean OR ... boolean OR M-K.
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2015-05
Language
English
Article Type
Article
Keywords

PERTURBED NEUMANN PROBLEM; POSITIVE BOUND-STATES; MULTI-BUMP SOLUTIONS; CRITICAL FREQUENCY; SEMICLASSICAL STATES; ELLIPTIC-EQUATIONS; RADIAL SOLUTIONS; EXISTENCE; POTENTIALS; SYMMETRY

Citation

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.14, no.3, pp.825 - 842

ISSN
1534-0392
DOI
10.3934/cpaa.2015.14.825
URI
http://hdl.handle.net/10203/200246
Appears in Collection
MA-Journal Papers(저널논문)
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