Existence of solutions for a critical fractional Kirchhoff type problem in RN

被引:32
|
作者
Xiang, MingQi [1 ]
Zhang, BinLin [2 ]
Qiu, Hong [1 ]
机构
[1] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
[2] Heilongjiang Inst Technol, Dept Math, Harbin 150050, Heilongjiang, Peoples R China
基金
中国国家自然科学基金;
关键词
fractional Laplacian; Kirchhoff problem; mountain pass theorem; Ekeland variational principle; BREZIS-NIRENBERG RESULT; LAPLACIAN EQUATIONS; NONLOCAL EQUATIONS;
D O I
10.1007/s11425-015-0792-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity: where (-Delta) (s) is the fractional Laplacian operator with 0 < s < 1, 2 (s) * = 2N/(N - 2s), N > 2s, p a (1, 2 (s) *), theta a [1, 2 (s) */2), h is a nonnegative function and lambda a real positive parameter. Using the Ekeland variational principle and the mountain pass theorem, we obtain the existence and multiplicity of solutions for the above problem for suitable parameter lambda > 0. Furthermore, under some appropriate assumptions, our result can be extended to the setting of a class of nonlocal integro-differential equations. The remarkable feature of this paper is the fact that the coefficient of fractional Laplace operator could be zero at zero, which implies that the above Kirchhoff problem is degenerate. Hence our results are new even in the Laplacian case.
引用
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页码:1647 / 1660
页数:14
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