Concentration phenomenon for fractional nonlinear Schrödinger equations

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 equationHere 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 z 0 of V , there is a nontrivial solution of equation (0.1) concentrating to z 0 as ε → 0. of science and engineering. For example, the thin obstacle problem [57,64], optimization

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