Electron. J. Differential Equations,
Vol. 2019 (2019), No. 24, pp. 122.
Multiplicity and concentration of positive solutions for fractional
nonlinear Schrodinger equations with critical growth
Xudong Shang, Jihui Zhang
Abstract:
In this article we consider the multiplicity and concentration
behavior of positive solutions for the fractional
nonlinear Schrodinger equation
where
is a positive parameter,
,
N >2s
and
is the fractional critical
exponent, and f is a
function satisfying
suitable assumptions. We assume that the potential
satisfies
, and that there exits k points
such that for each j=1,...,k,
are strictly global minimum. By using the variational method,
we show that there are at least k positive solutions for a small
>0.
Moreover, we establish the concentration
property of solutions as
tends to zero.
Submitted March 10, 2017. Published February 12, 2019.
Math Subject Classifications: 35A15, 58E05.
Key Words: Fractional Schrodinger equations; multiplicity of solutions;
critical growth; variational method.
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Xudong Shang
School of Mathematics
Nanjing Normal University
Taizhou College
225300, Jiangsu, China
email: xudongshang@163.com


Jihui Zhang
Jiangsu Key Laboratory for NSLSCS
School of Mathematical Sciences
Nanjing Normal University
Nanjing 210023, China
email: zhangjihui@njnu.edu.cn

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