The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of ...The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of three nonnegative solutions by means of the Leggett- Williams's fixed point theorem.展开更多
In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=...In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=0, I（y（c）,y′（c）,y″（c））=0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.展开更多
Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number...Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）展开更多
Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger...Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger’s inequality. The results, even restrictedto the case of differential equations, have generized and improved on the related results in[1]. Particularlyt a problem raised in Remark 5 in if] is answered definitely.展开更多
This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, suf...This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established展开更多
The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have o...The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]展开更多
We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of posit...We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].展开更多
Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point th...Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.展开更多
基金the Foundation of Educational Department of Shanghai City(No.05EZ52)
文摘The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of three nonnegative solutions by means of the Leggett- Williams's fixed point theorem.
基金Foundation item： the Natural Science Foundation of Fujian Province （No. S0650010）.
文摘In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=0, I（y（c）,y′（c）,y″（c））=0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.
基金the Natural Science Foundation of Gansu Province of China
文摘Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）
文摘Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger’s inequality. The results, even restrictedto the case of differential equations, have generized and improved on the related results in[1]. Particularlyt a problem raised in Remark 5 in if] is answered definitely.
基金the Tutorial Scientific Research Program Foundation of Education Department of Gansu Province (Nos. 0710-040810-03)
文摘This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established
文摘The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]
基金the Natural Science Foundation of Gansu Province(3ZS051-A25-016)NWNU-KJCXGCthe Spring-sun program(Z2004-1-62033).
文摘We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].
文摘Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
