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On the fractional Schrödinger problem with non‐symmetric potential
Author(s) -
Yang Jing
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3309
Subject(s) - mathematics , ground state , schrödinger equation , mathematical physics , state (computer science) , lyapunov function , reduction (mathematics) , schrödinger's cat , mathematical analysis , combinatorics , quantum mechanics , geometry , physics , nonlinear system , algorithm
We study the semilinear equation( − Δ ) s u + ( 1 + ϵV ( x ) ) u = u p ,u > 0inR N ,where 0 < s < 1, 1 < p < N + 2 s N − 2 s , V ( x ) is a sufficiently smooth non‐symmetric potential with V ( x ) ∈ L ∞ ( R N ) , and ϵ > 0 is a small number. Letting U be the radial ground state of (−Δ) s U + U − U p =0 inR N , we build solutions of the formu ( x ) ∼ ∑ j = 1 m U ( x − ϑ j )for points ϑ j , j = 1,⋯, m , using a Lyapunov–Schmidt variational reduction. Copyright © 2014 John Wiley & Sons, Ltd.
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