We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
CONCENTRATION PHENOMENON FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATIONS.
- Authors
GUOYUAN CHEN; YOUQUAN ZHENG; Juncheng Wei
- Abstract
We study the concentration phenomenon for solutions of the fractional nonlinear Schrödinger equation, which is nonlocal. We mainly use the Lyapunov-Schmidt reduction method. Precisely, consider the nonlinear equation (-ε² Δ)s v + Vv - |v|αv = 0 in Rn, (1) where n = 1, 2, 3, max{1/2, n/4} < s < 1, 1 ≤ α < α*(s,n), V ∈ Cb³(Rn. Here the exponent α*(s, n) = 4s/n - 2s for 0 < s < n/2 and α*(s, n) = ∞ for s ≥ n/2. Then for each non-degenerate critical point z0 of V, there is a nontrivial solution of equation (1) concentrating to z0 as ε → 0.
- Subjects
FRACTIONAL differential equations; SCHRODINGER equation; LYAPUNOV functions; NONLINEAR equations; NON-degenerate perturbation theory
- Publication
Communications on Pure & Applied Analysis, 2014, Vol 13, Issue 6, p2359
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2014.13.2359