This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, ...An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.展开更多
In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Pete...In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.展开更多
In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boun...In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.展开更多
In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） =...In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.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
Several eigenvalue properties of the third-order boundary value problems with distributional potentials are investigated.Firstly,we prove that the operators associated with the problems are self-adjoint and the corres...Several eigenvalue properties of the third-order boundary value problems with distributional potentials are investigated.Firstly,we prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real.Next,the continuity and differential properties of the eigenvalues of the problems are given,especially we find the differential expressions for the boundary conditions,the coefficient functions and the endpoints.Finally,we show a brief application to a kind of transmission boundary value problems of the problems studied here.展开更多
A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The auth...A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The authors show that the approximate so- lutions obtained by the numerical algorithm developed by using uonpolynomial quintic spline functions ave better than those produced by other spline and domain decomposition methods. The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach.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
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 some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two,...In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.展开更多
The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In orde...The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.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
In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the bound...In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.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
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.
基金The National Natural Science Foundation of China(11661071)
文摘In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.
文摘In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.
基金Supported by the HEBNSF of China(A2012506010)Supported by the YSF of Heibei Province(A2014506016)
文摘In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.
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supported by National Natural Science Foundation of China(No.12261066)the Natural Science Foundation of Inner Mongolia(No.2021MS01020 and No.2023LHMS01015).
文摘Several eigenvalue properties of the third-order boundary value problems with distributional potentials are investigated.Firstly,we prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real.Next,the continuity and differential properties of the eigenvalues of the problems are given,especially we find the differential expressions for the boundary conditions,the coefficient functions and the endpoints.Finally,we show a brief application to a kind of transmission boundary value problems of the problems studied here.
文摘A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The authors show that the approximate so- lutions obtained by the numerical algorithm developed by using uonpolynomial quintic spline functions ave better than those produced by other spline and domain decomposition methods. The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach.
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.
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.
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the National Natural Science Foundation of China(11261053)The Natural Science Foundation of Gansu Province(1308RJZA125)
文摘In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.
基金The paper is supported by NNSFC (10471155)SRFDP (20020558092) SFGD (031608).
文摘The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.
基金Natural Science Foundation of Fujian Province under grant No.S0650010the Foundation of the Education Department of Fujian Province (JB06098).
文摘The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.
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Supported by the National Natural Science Foundation of China(No.11126245)PHR(IHLB)Funding Project for Young and Middle-aged Backbone Teachers of Beijing Union University
文摘In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.
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.
