Periodic boundary value problems for impulsive fuzzy differential equations

The peculiarity of the Hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations. In this work, we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method. Fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic ‘linear’ differential problems is also provided.     

Periodic boundary value problem for first-order impulsive ordinary differential equations

This paper investigates the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive differential equations by establishing two comparison results and using the method of upper and lower solutions and the monotone iterative technique.     

Non-linear functional boundary value problem for discontinuous functional differential equations

This paper is devoted to investigating the existence of solutionsfor discontinuous functional differential equations with non-linearfunctional boundary conditions. Some existence results of solutionsare obtained by employing a generalized method of upper andlower solutions, which may be discontinuous.     

Periodic boundary value problem for the first order functional differential equations with impulses

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.     

Nonlinear boundary value problem of first order impulsive functional differential equations

This paper discusses nonlinear boundary value problem for first order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. Two examples are discussed to illustrate the efficiency of the obtained results.     

Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations

This paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations

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Periodic boundary value problems for first order impulsive integro-differential equations of mixed type

This paper investigates the existence of minimal and maximal solutions of periodic boundary value problem for first order impulsive integro-differential equations of mixed type by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique.     

New comparison results for impulsive integro-differential equations and applications

We prove some new maximum principles for ordinary integro-differential equations. This allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first-order impulsive integro-differential equation.     

Boundary value problem of second order impulsive functional differential equations

This paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. An example is discussed to illustrate the efficiency of the obtained result.     

Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions

This paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions. By establishing new comparison results and applying the monotone iterative technique, we obtain the sufficient conditions for the existence of extremal system of solutions.     

Impulsive periodic boundary value problems of first-order differential equations

In this paper, by using Schaeffer's theorem, we prove new existence theorems for a nonlinear periodic boundary value problem of first-order differential equations with impulses. Our results improve and generalize some known results.     

Study of singular boundary value problems for second order impulsive differential equations

This paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established.     

Periodic solutions for ordinary differential equations with sublinear impulsive effects

The continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects. The applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations, for instance, the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with Landesman-Lazer conditions.     

Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type

This paper discusses nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. The lower and upper solutions and monotone iterative techniques are used to achieve the existence results. Two examples are provided to illustrate the efficiency of the obtained results.     

单调迭代法与一阶脉冲泛函微分方程周期边值问题

本文利用单调迭代法与上下解方法,研究了一阶脉冲泛函做分方程周期边值问题最大解与最小解的存在性.     

Periodic solutions of delay impulsive differential equations

We study the following semilinear impulsive differential equation with delay:

     

Integral boundary value problems for first order nonlinear impulsive functional integro-differential differential equations

In this paper, we consider the existence of solutions for first order nonlinear impulsive functional integro-differential equations with integral boundary value conditions. We firstly build a new comparison theorem. Then by utilizing the monotone iterative technique and the method of lower and upper solutions, we obtain the existence of extremal solutions or quasi-solutions.     

Impulsive anti-periodic boundary value problem of first-order integro-differential equations

This paper is concerned with the anti-periodic boundary value problem of first-order nonlinear impulsive integro-differential equations. We first establish a new comparison principle, and then obtain the existence of extremal solutions by upper-lower solution and monotone iterative techniques. Some examples are presented to illustrate the main results.     

On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations

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 of first and second order periodic boundary value problems and periodic solutions of functional differential equations. We obtain some new results relative to the lower solution α and upper solution β with α?β.