Electron. J. Differential Equations,
Vol. 2019 (2019), No. 102, pp. 116.
Nontrivial solutions of fractional SchrodingerPoisson systems
with sum of periodic and vanishing potentials
Mingzhu Yu, Haibo Chen
Abstract:
We consider the fractional SchrodingerPoisson system
where
,
,
,
K(x),
and f(x,u) are periodic in x, V is coercive or
is a sum of a periodic potential
and a localized potential
.
If f has the subcritical growth,
but higher than
,
we establish the existence and
nonexistence of ground state solutions are dependent on the sign of
.
Moreover, we prove that such a problem admits infinitely many pairs of
geometrically distinct solutions provided that V is periodic and f
is odd in u. Finally, we investigate the existence of ground state solutions
in the case of coercive potential V.
Submitted March 22, 2018. Published September 4, 2019.
Math Subject Classifications: 35B38, 35G99.
Key Words: Fractional SchrodingerPoisson system; coercive potential;
periodic and localized potential; Nehari manifold; variational method.
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Mingzhu Yu
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: yumz_math@csu.edu.cn


Haibo Chen
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: math_chb@163.com

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