This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum p...This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.展开更多
A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan’s preconditioner cU (An) from the viewpoint of the...A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan’s preconditioner cU (An) from the viewpoint of the numerical range. An application in numerical ODEs is also given.展开更多
A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value prob...A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in ...Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.展开更多
By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′...By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.展开更多
By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,...By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.展开更多
In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
Abstract： In this paper, we study the existence of a solution for fifth-order boundary value problem{u（5）（t）＋f（t,u（t）,u＂（t）=0,0〈t〈1）/u（0）=u＇（0）=u＇（1）=u＂（1）=u（4）（0）=0 Where f ∈ C（[0,1] &...Abstract： In this paper, we study the existence of a solution for fifth-order boundary value problem{u（5）（t）＋f（t,u（t）,u＂（t）=0,0〈t〈1）/u（0）=u＇（0）=u＇（1）=u＂（1）=u（4）（0）=0 Where f ∈ C（[0,1] × R2, R）. By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary value problem with the use of the lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solution is also present.ed. Boundary value problems of very similar type are also considered.展开更多
By applying the fixed-point theorem of strict-set-contraction,this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach s...By applying the fixed-point theorem of strict-set-contraction,this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach spaces.展开更多
By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee ...By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.展开更多
In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certa...In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.展开更多
In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a cla...In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.展开更多
In this paper, we study the nonlinear singular boundary value problems in Banach spaces：-x=f（t,x）,t∈（0,1）,a1x（0）-a2x＇（0）=θ,b1x（1）＋b2x＇（1）=θ.where θ denotes the zero element of E, E is a real Banach...In this paper, we study the nonlinear singular boundary value problems in Banach spaces：-x=f（t,x）,t∈（0,1）,a1x（0）-a2x＇（0）=θ,b1x（1）＋b2x＇（1）=θ.where θ denotes the zero element of E, E is a real Banach space, and f （t, x） is allowed to be singular at both end point t = 0 and t = 1. We show the existence of at least two positive solutions of this problem.展开更多
This paper proves a Filippov type existence theorem for solutions of a boundary valueproblem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued map.Themethod consists in application of...This paper proves a Filippov type existence theorem for solutions of a boundary valueproblem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued map.Themethod consists in application of the contraction principle in the space of selections of the set-valuedmap instead of the space of solutions.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
This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and th...This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.展开更多
基金supported by the National Natural Science Foundation of China (No.12061078)。
文摘This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.
基金The research is partially supported by the grant RG081/04-05S/JXQ/FST from University of Macao and thegrant 050/2005/A from FDCT.
文摘A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan’s preconditioner cU (An) from the viewpoint of the numerical range. An application in numerical ODEs is also given.
文摘A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
基金Foundation item： Supported by Natural Science Foundation of China（60675022）
文摘Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.
文摘By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671167） Supported by the Research Foundation of Liaocheng University（31805）
文摘By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.
基金Supported by Nature Science Foundation of Education Department of Henan Province（2010A110023）
文摘In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
文摘Abstract： In this paper, we study the existence of a solution for fifth-order boundary value problem{u（5）（t）＋f（t,u（t）,u＂（t）=0,0〈t〈1）/u（0）=u＇（0）=u＇（1）=u＂（1）=u（4）（0）=0 Where f ∈ C（[0,1] × R2, R）. By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary value problem with the use of the lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solution is also present.ed. Boundary value problems of very similar type are also considered.
基金Supported by the Research Project of Bozhou Teacher’s College(BSKY0805)Supported by the Natural Science Research Project of Anhui Province(KJ2009B093)
文摘By applying the fixed-point theorem of strict-set-contraction,this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach spaces.
基金Foundation item： Supported by the National Natural Science Foundation of China（10801001） Supported by the Natural Science Foundation of Anhui Province（1208085MA13）
文摘By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.
文摘In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
文摘In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained.
基金the "Qing-Lan" Project of Jiangsu Education Committee and the Natural Science Foundation of Jiangsu Education Committee, China (02KJD460011)
文摘In this paper, we study the nonlinear singular boundary value problems in Banach spaces：-x=f（t,x）,t∈（0,1）,a1x（0）-a2x＇（0）=θ,b1x（1）＋b2x＇（1）=θ.where θ denotes the zero element of E, E is a real Banach space, and f （t, x） is allowed to be singular at both end point t = 0 and t = 1. We show the existence of at least two positive solutions of this problem.
文摘This paper proves a Filippov type existence theorem for solutions of a boundary valueproblem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued map.Themethod consists in application of the contraction principle in the space of selections of the set-valuedmap instead of the space of solutions.
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
基金supported by the National Natural Science Foundation of China(No.11171220)the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Hujiang Foundation of China(No.B14005)
文摘This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.
