Existence p results of positive solutions for Kirchhoff type biharmonic equation via bifurcation methods

doi:10.3906/mat-2001-50

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	Existence p results of positive solutions for Kirchhoff type biharmonic equation via bifurcation methods
	Wang, Jinxiang; Wang, Da-Bin
刊名	TURKISH JOURNAL OF MATHEMATICS
	2020
卷号	44 期号:5 页码:1824-1834
关键词	Kirchhoff type biharmonic equation global bifurcation positive solution
ISSN号	1300-0098
DOI	10.3906/mat-2001-50
英文摘要	This paper is concerned with the existence of positive solutions for the fourth order Kirchhoff type problem {Delta(2)u - (a + b integral Omega vertical bar Vu vertical bar(2)dx)Delta u = lambda f (u(x)), in Omega, u = Delta u = 0, on partial derivative Omega, where Omega C R-N (N >= 1) is a bounded domain with smooth boundary partial derivative Omega, a > 0, b >= 0 are constants, lambda is an element of R is a parameter. For the case f (u) equivalent to u, we use an argument based on the linear eigenvalue problems of fourth order elliptic equations to show that there exists a unique positive solution for all lambda > Lambda(1,a), here Lambda(1,a) is the first eigenvalue of the above problem with b = 0; For the case f is sublinear, we prove that there exists a positive solution for all lambda > 0 and no positive solution for lambda < 0 by using bifurcation method.
WOS研究方向	Mathematics
语种	英语
出版者	SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK
WOS记录号	WOS:000575368100024
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/155260]
专题	理学院
作者单位	Lanzhou Univ Technol, Dept Appl Math, Lanzhou, Peoples R China
推荐引用方式 GB/T 7714	Wang, Jinxiang,Wang, Da-Bin. Existence p results of positive solutions for Kirchhoff type biharmonic equation via bifurcation methods[J]. TURKISH JOURNAL OF MATHEMATICS,2020,44(5):1824-1834.
APA	Wang, Jinxiang,&Wang, Da-Bin.(2020).Existence p results of positive solutions for Kirchhoff type biharmonic equation via bifurcation methods.TURKISH JOURNAL OF MATHEMATICS,44(5),1824-1834.
MLA	Wang, Jinxiang,et al."Existence p results of positive solutions for Kirchhoff type biharmonic equation via bifurcation methods".TURKISH JOURNAL OF MATHEMATICS 44.5(2020):1824-1834.