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刘斌, Bing Liu
B Liu/Nonlinear Analysis 64(2006)1336-1355,-0001,():
-1年11月30日
In this paper, by using the fixed points of strict-set contractions, we study the existence of at least one or two positive solutions to the second-order three-point boundary value problem y''(t)+a(t)ƒ(y(t))=θ, 0<t<1, y(0)=θ, y(1)=βy(η) in Banach space E, where θ is the zero element of E, 0<β<1, 0<η<1 and a (t) is allowed to change sign on [0, 1]. As an application, we also give one example to demonstrate our results.
Banach space, Positive solution, Fixed point, Three-point boundary value problems
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刘斌, Bing Liu
B Liu/Nonlinear Analysis 66(2007)1661-1674,-0001,():
-1年11月30日
In this paper, by using the fixed points of strict-set-contractions, we study the existence of at least one or two positive solutions to the generalize Sturm-Liouville four-point boundary value problem y''(t)+a(t)f(y (t))=θ, 0<t<1, αy(0)-βy1(0)=μ1y(ξ), γy(1)+δy'(1)=μ2y(η), in Banach space E, where θ is the zero element of E, 0<ξ<1, 0<η<1. As an application, we also give an example to demonstrate our results.
Banach space, Positive solution, Fixed point, Sturm-Liouville, Four-point boundary value problems
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35浏览
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刘斌, BING LIU
Applied Maqthematics Letters 17(2004)655-661,-0001,():
-1年11月30日
We consider the singular three-point boundary value problems (Φp (y'))'+a(t)ƒ(y (t))=0, 0<t<1, y' (0)=0, y (1)=βy (n), where Φp (s)=|s|p-2s, p>2, 0<β< 1, 0<η< 1, f ∈ C ((0,+∞), (0,+∞)), a: (0, 1)~(0,+∞), and has countably many singularities in (0, 1/2). We show that there exist countably many positive solutions by using the fixed-point index theory.
Singularity,, One-dimensional p-Laplacian,, Multiple positive solutions,, Three-point boundary value problems,, Fixed-point index.,
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【期刊论文】Solvability of multi-point boundary value problem at resonance--Part IV☆
刘斌, Bing Liu
B. Liu/Appl. Math. Comput. 143(2003)275-299,-0001,():
-1年11月30日
In this paper, we consider the following second order ordinary differential equation x''=ƒ(t, x (t),x'(t))+e(t), t∈(0, 1), (1.1) subject to one of the following boundary value conditions: x(0)=m-2∑i=1/αix(ξi), x(1)=n-2∑j=1/βjx(ηj), (1.2) x'(0)=m-2∑i=1/αix1 (ξi), x'(1)=n-2∑j=1/βjx1 (ηj), (1.3) x'(0)=m-2∑i=1/αix1 (ξi), x'(1)=n-2∑j=1/βjx (ηj), (1.4) where αi (1≤i≤m-2), βj (1≤j≤n-2) ∈ R, 0<ξ1<ξ2<……<ξm-2<1, 0<η1<η2<……<ηn-2< 1. When all the ais have no the same sign and all the bjs have no the same sign, some existence results are given for (1.1) with boundary conditions (1.2)-(1.4) at resonance case. We also give some examples to demonstrate our results.
Boundary value problems, Fredholm operator, Resonance, Coincidence degree
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【期刊论文】Periodic solutions of a nonlinear second-order differential equation with deviating argument
刘斌, Bing Liu
B. Liu/J. Math, Anal, Appl. 309(2005)313-321,-0001,():
-1年11月30日
With the help of the coincidence degree continuation theorem, the xistence of periodic solutions of a nonlinear second-order differential equation with deviating argument x''(t)+ƒ1(x(t)x'(t+ƒ2(x(t))(x'(t))2+g(x(t-r(t))=0, under some assumptions are obtained.
Periodic solutions, Coincidence degree continuation theorem, Deviating argument
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