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 existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The ...The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The interest is that the nonlinear term may be展开更多
In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems ...In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems.展开更多
In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1）...In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1） =sum （μiDpu（t）｜t = ξi ） from i =1 to ∞ m-2, where q ∈R , 1 q ≤2 , 0 ξ1 ξ2 ··· ξm-2 ≤ 1/2 , μi ∈[0 , ＋∞） and p = q-1/2 , Γ（q） sum （μiξi（q-1）/2 Γ（（ q＋1）/2） from i =1 to ∞ m-2,Dq is the standard Riemann-Liouville differentiation, and f ∈C （[0 , 1]×[0 , ＋∞） , [0 , ＋∞））. By using the Leggett-Williams fixed point theorem on a convex cone, some multiplicity results of positive solutions are obtained.展开更多
In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel’skii fixed-point theor...In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel’skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.展开更多
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ...In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ i ）） from i=1 to m-2, u（1）= sum （aiu（ξ i ）） from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞） and f （t, u） ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.展开更多
By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also ...By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also given.展开更多
By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to s...In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.展开更多
Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these probl...Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.展开更多
By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green’s funct...By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green’s functions of the problems are also given.展开更多
By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main...By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.展开更多
By using Mawhin＇s continuation theorem, the existence of solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main r...By using Mawhin＇s continuation theorem, the existence of solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of the paper.展开更多
In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,.....In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).展开更多
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new...Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.展开更多
A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0,...A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.展开更多
By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>...By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.展开更多
This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditi...This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.展开更多
The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our ...The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.展开更多
A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhi...A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.展开更多
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 Natural Science Foundation of Hebei Province of China(No.A2006000298)the Doctoral Foundation of Hebei Province of China(No.B2004204)
文摘The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The interest is that the nonlinear term may be
文摘In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems.
基金supported by Hunan Provincial Natural Science Foundation of China(11JJ3009)supported by the Scientific Research Foundation of Hunan Provincial Education Department(11C1187)the Construct Program of the Key Discipline in Hunan Province
文摘In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations： Dqu（t） ＋ f（t, u（t）） = 0, 0 t 1, u（0） = 0, u（1） =sum （μiDpu（t）｜t = ξi ） from i =1 to ∞ m-2, where q ∈R , 1 q ≤2 , 0 ξ1 ξ2 ··· ξm-2 ≤ 1/2 , μi ∈[0 , ＋∞） and p = q-1/2 , Γ（q） sum （μiξi（q-1）/2 Γ（（ q＋1）/2） from i =1 to ∞ m-2,Dq is the standard Riemann-Liouville differentiation, and f ∈C （[0 , 1]×[0 , ＋∞） , [0 , ＋∞））. By using the Leggett-Williams fixed point theorem on a convex cone, some multiplicity results of positive solutions are obtained.
基金supported by the National Natural Science Foundation of China (10971173)the Natural Science Foundation of Hunan Province (10JJ3096)
文摘In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel’skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.
基金Supported by Fund of National Natural Science of China (No. 10371068)Science Foundation of Business College of Shanxi University (No. 2008053)
文摘In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ i ）） from i=1 to m-2, u（1）= sum （aiu（ξ i ）） from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞） and f （t, u） ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
文摘By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also given.
基金the Natural Science Foundation of Anhui Educational Department(Kj2007b055) Youth Project Foundation of Anhui Educational Department(2007jqL101,2007jqL102)
文摘By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
基金Sponsored by the National Natural Science Foundation of China (No.10971238)
文摘In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.
基金sponsored by Natural Science Foundation of Anhui Educational Department(Kj2007b055) Youth Project Foundation of Anhui Educational Department (2007jqL1012007jqL102)
文摘Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.
基金sponsored by the Natural Science Foundation of Anhui Educational Department(KJ2009B100)Youth Project Foundation of Anhui Educational Department (2009SQRZ155)
文摘By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green’s functions of the problems are also given.
基金The NSF (Kj2007b055) of Anhui Educational Departmentthe Youth Project Foundation (2007jqL101,2007jqL102) of Anhui Educational Department.
文摘By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.
基金The work is sponsored by Youth Project Foundation of Anhui Educational Dept.(2007jqL101,2007jqL102)Natural Science Foundation of Anhui Educational Dept.(kj2007b055).
文摘By using Mawhin＇s continuation theorem, the existence of solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of the paper.
文摘In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).
基金Project supported by the National Natural Science Foundation of China (No.10371006)
文摘Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.
文摘A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.
文摘By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.
基金Supported by the NSF of Jiangsu Province(BK2008119)the NSF of the Education Department of Jiangsu Province (08KJB110011)+1 种基金Innovation Project of Jiangsu Province Postgraduate Training Project(CX07S 015z)the Qinglan Program of Jiangsu Province (QL200613)
文摘This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.
文摘The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.
基金National Natural Science Foundation of China(No.11271248)
文摘A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.
