Existence and uniqueness of positive solutions for Kirchhoff type beam equations

doi:10.14232/ejqtde.2020.1.61

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	Existence and uniqueness of positive solutions for Kirchhoff type beam equations
	Wang, Jinxiang
刊名	ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
	2020
期号	61 页码:1-14
关键词	fourth order boundary value problem Kirchhoff type beam equation global bifurcation positive solution uniqueness
ISSN号	1417-3875
DOI	10.14232/ejqtde.2020.1.61
英文摘要	This paper is concerned with the existence and uniqueness of positive solutions for the fourth order Kirchhoff type problem {u ''''(x) - (a+b integral(1)(0)(u'(x))(2)dx)u ''(x) =lambda f(u(x)), x is an element of (0,1), i(0) = u(1) = u ''(0) u ''(1) = 0, where a > 0, b >= 0 are constants, lambda is an element of R is a parameter. For the case f (u) = u, we use an argument based on the linear eigenvalue problems of fourth order equations and their properties 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 unique positive solution for all lambda > 0 and no positive solution for l < 0 by using bifurcation method.
WOS研究方向	Mathematics
语种	英语
出版者	UNIV SZEGED, BOLYAI INSTITUTE
WOS记录号	WOS:000583805500001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/155258]
专题	理学院
作者单位	Lanzhou Univ Technol, Dept Appl Math, 287 Langongping Rd, Lanzhou, Peoples R China
推荐引用方式 GB/T 7714	Wang, Jinxiang. Existence and uniqueness of positive solutions for Kirchhoff type beam equations[J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS,2020(61):1-14.
APA	Wang, Jinxiang.(2020).Existence and uniqueness of positive solutions for Kirchhoff type beam equations.ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS(61),1-14.
MLA	Wang, Jinxiang."Existence and uniqueness of positive solutions for Kirchhoff type beam equations".ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS .61(2020):1-14.