SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N  

作　　者：Kun CHENG Qi GAO 程琨;高琦

机构地区：[1]Department of Information Engineering, Jingdezhen Ceramic Institute [2]Department of Mathematics, School of Science, Wuhan University of Technology

出　　处：《Acta Mathematica Scientia》2018年第6期1712-1730,共19页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11501231);the "Fundamental Research Funds for the Central Universities"(WUT2017IVA077,2018IB014)

摘　　要：In this paper, we study the existence of least energy sign-changing solutions for aKirchhoff-type problem involving the fractional Laplacian operator. By using the constraintvariation method and quantitative deformation lemma, we obtain a least energy nodal solu-tion ub for the given problem. Moreover, we show that the energy of ub is strictly larger thantwice the ground state energy. We also give a convergence property of ub as b O, where bis regarded as a positive parameter.In this paper, we study the existence of least energy sign-changing solutions for aKirchhoff-type problem involving the fractional Laplacian operator. By using the constraintvariation method and quantitative deformation lemma, we obtain a least energy nodal solu-tion ub for the given problem. Moreover, we show that the energy of ub is strictly larger thantwice the ground state energy. We also give a convergence property of ub as b O, where bis regarded as a positive parameter.

关 键 词：Kirchhoff equation fractional Laplaciau sign-changing solutions 

分 类 号：O175[理学—数学]