In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with r...This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.展开更多
The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsi...This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.展开更多
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mi...This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.展开更多
In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain exist...In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an ...The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.展开更多
In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative...In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.展开更多
An iterative process of positive solution for BVP w'+h(t)f(w)=0, w(0)=w(1)= 0 is established, where h(t) is allowed to changes sign on [0,1]. The process starts from a simple function.
In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower...In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower solution a with β a.展开更多
In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal...In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equatio...The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.展开更多
This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existenc...This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.展开更多
In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a un...In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a unique solution or extremal ones to the given problem.A monotone iterative technique is applied.展开更多
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem ...The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations.展开更多
The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order i...The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order impulsive differential equation.展开更多
This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficien...This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.展开更多
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
文摘This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.
文摘The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
文摘This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
文摘This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.
文摘In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.
文摘In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.
文摘An iterative process of positive solution for BVP w'+h(t)f(w)=0, w(0)=w(1)= 0 is established, where h(t) is allowed to changes sign on [0,1]. The process starts from a simple function.
文摘In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower solution a with β a.
基金Research supported by the NSF of Shandong Province (Y2004A01) the foundation of SDAI(XN040101).
文摘In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.
基金Supported partially by the Youthful Sciences Foundation of Shanxi(20021003).
文摘The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.
基金Research supported by the Foundation of Department of Science and Technology of Fujian Province (K2001104).
文摘This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.
基金This work was supported by the National Natural Science Foundation of China (10571050)Hunan Provincial Natural Science Foundation of China (05JJ40013)and Scientific Research Fund of Hunan Provincial Education Department (05C413).
文摘In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a unique solution or extremal ones to the given problem.A monotone iterative technique is applied.
文摘The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations.
基金This work is supported by the National Natural Sciences Foundation of China(10471040) the Sciences Foundation of Shanxi (2005Z010) the Major Subject Foundation of Shanxi (20055024).
文摘The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order impulsive differential equation.
基金supported by Scientific Research Fund of Hunan Provincial Education Department (10C0258)
文摘This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.
