@article{An2022, 
author = {Xiaoming An and Shuangjie Peng},
title = {Multi-peak semiclassical bound states  for Fractional Schrödinger Equations with fast decaying potentials},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {2},
pages = {585-614},
keywords = {variational method, fractional Schrödinger, multi-peak, compactly supported, penalized technique},
url = {https://www.sciopen.com/article/10.3934/era.2022031},
doi = {10.3934/era.2022031},
abstract = {We study the following fractional Schrödinger equation    ε2s(−Δ)su+V(x)u=f(u),x∈RN,where  s∈(0,1). Under some conditions on  f(u), we show that the problem has a family of solutions concentrating at any finite given local minima of  V provided that  V∈C(RN,[0,+∞)). All decay rates of  V are admissible. Especially,  V can be compactly supported.  Different from the local case  s=1 or the case of single-peak solutions, the nonlocal effect of the operator  (−Δ)s makes the peaks of the candidate solutions affect mutually, which causes more difficulties in finding solutions with multiple bumps. The methods in this paper are penalized technique and variational method.}
}