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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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【期刊论文】Positive solutions of a nonlinear four-point boundary value problems in Banach spaces
刘斌, Bing Liu
B. Liu/J. Math. Anal, Appl. 305(2005)253-276,-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 four-point boundary value problem y''(t)+a(t)f(y(t)=θ, 0<t<1, y(0)=μy(ξ), y(1)=βy(η) in Banach space E, where θ is zero element of E, 0<ξ≤η< 1, 0<μ< 1/1−ξ, 0<β<1/η and μξ(1-β)+(1-μ)(1-βη)>0. As an application, we also give one example to demonstrate our results.
Banach space, Positive solution, Fixed point, Four-point boundary value problems
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36浏览
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【期刊论文】Existence and Uniqueness of Solutions to First-Order Multipoint Boundary Value Problems
刘斌, BING LIU
Applied Mathematics Letters 17(2004)130-1316,-0001,():
-1年11月30日
this paper, we give existence and uniqueness results for solutions of multipoint boundary value problems of the form x'=ƒ(t,x(t))+e(t), t∈(0,1), m∑j=1/Ajx (ηj)=0, where ƒ: [0, 1] x Rn→Rn is s Carathdodory function, Ajs (j=1, 2,……,m) are constant square matrices of order n1, 0<η1<η2<…<ηm-1<ηm<1, and e(t) ∈L1([0, 1], Rn). The existence of solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results.
First-order system, Existence and uniqueness of solution, Multipoint boundary value problems, Fredholm operator, Coincidence degree.,
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30浏览
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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】Controllability of Nonlinear Neutral Evolution Integrodifferential Systems with Infinite Delay
刘斌, B. Liu
JOTA: VOL. 122, NO.1, JULY 2004, 99-109,-0001,():
-1年11月30日
Sufficient conditions are derived for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in a Banach space. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An example is given to illustrate the results.
Controllability, mild solutions, resolvent operators, neutral evolution integrodifferential systems, infinite delays.,
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