EXISTENCE RESULTS FOR SINGULAR FRACTIONAL p-KIRCHHOFF PROBLEMS

作     者：Mingqi XIANG Vicent iu D.RADULESCU Binlin ZHANG 向明启;Vicent iu D.RADULESCU;张彬林

作者机构：College of ScienceCivil Aviation University of ChinaTianjin 300300China Faculty of Applied MathematicsAGH University of Science and Technologyal.Mickiewicza 3030-059 Krak´owPoland Department of MathematicsUniversity of CraiovaStreet A.I.Cuza No.13200585 CraiovaRomania Institute of MathematicsPhysics and MechanicsJadranska 191000 LjubljanaSlovenia College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdao 266590China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第3期

页      面：1209-1224页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(11601515) Fundamental Research Funds for the Central Universities(3122017080) the second author acknowledges the support of the Slovenian Research Agency grants P1-0292,J1-8131,N1-0064,N1-0083,N1-0114 the third author was supported by National Natural Science Foundation of China(11871199and 12171152) Shandong Provincial Natural Science Foundation,PR China(ZR2020MA006) Cultivation Project of Young and Innovative Talents in Universities of Shandong Province 

主　　题：Fractional Kirchhoff equation singular problems variational and topological methods 

摘      要：This paper is concerned with the existence and multiplicity of solutions for singular Kirchhoff-type problems involving the fractional p-Laplacian *** precisely,we study the following nonlocal problem:{M (∫∫_(R2N)|x|^(α1p)|y|^(α2p)|u(x) − u(y)|^(p)/|x − y|^(N+ps) dxdy)L_(p)^(s)u = |x| ^(β)f(u) in Ω,u = 0 in R^(N) \ Ω,where L_(p)^(s) is the generalized fractional p-Laplacian operator,N≥1,s∈(0,1),α_(1),α_(2),β∈R,Ω■R^(N) is a bounded domain with Lipschitz boundary,and M:R0^(+)→R0^(+),f:Ω→R are continuous ***,we introduce a variational framework for the above ***,the existence of least energy solutions is obtained by using variational methods,provided that the nonlinear term f has(θ_(p-1))-sublinear growth at ***,the existence of infinitely many solutions is obtained by using Krasnoselskii’s genus ***,we obtain the existence and multiplicity of solutions if f has(θ_(p-1))-superlinear growth at *** main features of our paper are that the Kirchhoff function may vanish at zero and the nonlinearity may be singular.