In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assumi...In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.展开更多
The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ...The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].展开更多
In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions...In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.展开更多
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existen...By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.展开更多
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing t...The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.展开更多
This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the differe...This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.展开更多
This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a cl...This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41(2), 211-220 (1999]]. Some known results are operators.展开更多
In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second ord...In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.展开更多
基金The NSF(201701D0503-9)of Shanxi Provincethe Innovation Foundation for College Teaching Team of Shanxi University of Finance and Economics2015 Education and Teaching Reform Project(2015234)of Shanxi University of Finance and Economics
文摘In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.
基金Supported by National Natural Science Foundation of China
文摘The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].
文摘In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.
基金supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032)the National Natural Science Foundation of China (10571021, 10701020)
文摘By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.
基金The Innovation Foundation for College Research Team of Shanxi University of Finance and Economics
文摘The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.
基金Supported by the Foundation for Students Innovative Projects of Heilongjiang Province(201510234012)
文摘This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.
基金the National Natural Science Foundation of China (10371010) and RFDP
文摘This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41(2), 211-220 (1999]]. Some known results are operators.
基金Project supported financially by the National Natural Science Foundation of China (1087111610671167)
文摘In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.