Li Wang, Binlin Zhang
Abstract:
In this article, we show the existence of infinitely many solutions for the
fractional p-Laplacian equations of Schrodinger-Kirchhoff type equation
where
is the fractional p-Laplacian operator,
is the Gagliardo p-seminorm,
,
,
,
M is a continuous and positive function, V is a continuous
and positive potential function and k(x) is a non-negative function in
an appropriate Lebesgue space. By means of the concentration-compactness
principle in fractional Sobolev space and Kajikiya's new version of the
symmetric mountain pass lemma, we obtain the existence of infinitely many
solutions which tend to zero for suitable positive parameters
and
.
Submitted October 11, 2016. Published December 30, 2016.
Math Subject Classifications: 35R11, 35A15, 47G20.
Key Words: Schrodinger-Kirchhoff type equation; fractional p-Laplacian;
critical Sobolev exponent.
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Li Wang School of Basic Science East China Jiaotong University Nanchang 330013, China email: wangli.423@163.com | |
Binlin Zhang Department of Mathematics Heilongjiang Institute of Technology Harbin 150050, China email: zhangbinlin2012@163.com |
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