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期刊名称: Nonlinearity
Volume:29    Issue:2        Page:357-374
ISSN:0951-7715

Infinitely many solutions for the stationary Kirchhoff problems involving the fractional p-Laplacian期刊论文

作者: Mingqi Xiang Bisci Giovanni Molica Tian Guohua Zhang Binlin
DOI:10.1088/0951-7715/29/2/357

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页码: 357-374
被引频次: 53
出版者: IOP PUBLISHING LTD
期刊名称: Nonlinearity
ISSN: 0951-7715
卷期: Volume:29    Issue:2
语言: English
摘要: The aim of this paper is to establish the multiplicity of weak solutions for a Kirchhoff-type problem driven by a fractional p-Laplacian operator with homogeneous Dirichlet boundary conditions: {M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(N+ps)dxdy)(-Delta)(p)(s)u(x) = f(x, u) in Omega u=0 in R-N/Omega where Omega is an open bounded subset of R-N with Lipshcitz boundary partial derivative Omega, (-Delta)(p)(s) is the fractional p-Laplacian operator with 0 < s < 1 < p < N such that sp < N, M is a continuous function and f is a Caratheodory function satisfying the Ambrosetti-Rabinowitz-type condition. When f satisfies the suplinear growth condition, we obtain the existence of a sequence of nontrivial solutions by using the symmetric mountain pass theorem; when f satisfies the sublinear growth condition, we obtain infinitely many pairs of nontrivial solutions by applying the Krasnoselskii genus theory. Our results cover the degenerate case in the fractional setting: the Kirchhoff function M can be zero at zero.
相关主题: symmetric mountain pass theorem, fractional p-Laplacian, infinitely many solutions, genus theory, Kirchhoff-type problem, EXISTENCE, MATHEMATICS, APPLIED, MULTIPLICITY, EXPONENT, PHYSICS, MATHEMATICAL, NONLOCAL OPERATORS,

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