By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,...By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.展开更多
We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1...We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.展开更多
In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δl...In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δlimt→＋∞p（t）x′（t）=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.展开更多
Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive...Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.展开更多
The singular boundary value problem{φ^（4）（x）-h（x）f（φ（x））=0,0〈x〈1, φ（0）=φ（1）=φ′（0）=φ′（1）=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant ...The singular boundary value problem{φ^（4）（x）-h（x）f（φ（x））=0,0〈x〈1, φ（0）=φ（1）=φ′（0）=φ′（1）=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant linear operators, where h（x） is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10671167） Supported by the Research Foundation of Liaocheng University（31805）
文摘By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.
基金Supported by the National Natural Science Foundation of China(10371006)
文摘We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.
基金Supported by the Natural Scientific Fund of Zhejiang Province(Y604127)Supported by the Educational Scientific Fund of Zhejiang Province(20030594)
文摘In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δlimt→＋∞p（t）x′（t）=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.
文摘Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.
基金the National Natural Science Foundation of China （No. 10671167） the Chunlei Program of SDUST （No. 2008AZZ044）.
文摘The singular boundary value problem{φ^（4）（x）-h（x）f（φ（x））=0,0〈x〈1, φ（0）=φ（1）=φ′（0）=φ′（1）=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant linear operators, where h（x） is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index.
