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.     

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.     

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.     

Boundary value problem for first order impulsive functional integro-differential equations

This paper investigates extremal solutions of the boundary value problem for impulsive functional integro-differential equations with nonlinear boundary conditions and deviating arguments. In the presence of a lower solution u and an upper solution v with u≥v, existence of extremal solutions is proved by establishing a new comparison principle and using the monotone iterative technique.     

Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations

We consider a class of first-order impulsive functional differential equations, where the functional dependence is not necessarily a Lipschitzian function. The new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented. We give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution.     

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

In this paper, by means of the method of upper and lower solutions and the monotone iterative technique, the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive functional differential equations is considered.     

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.     

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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Nonlinear boundary problem of first order impulsive integro-differential equations

This paper focuses on first-order impulsive integro-differential equations with nonlinear boundary. The lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem. Numerical examples are given to prove its validity.     

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.     

Boundary value problems for first order functional differential equations with impulsive integral conditions

In this paper, by using the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition. Some comparison results are also formulated.     

Anti-periodic solutions of nonlinear first order impulsive functional differential equations

The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$ x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z} $$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.     

Quasilinearization of a boundary value problem for impulsive differential equations

In this paper we study the existence and approximation of solution for nonlinear impulsive differential equations with fixed moments of impulsive perturbations. Using quasilinearization technique we obtain a monotone sequence of approximate solutions that converges quadratically to a solution.     

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.     

Multiplicity of positive solutions to M-point boundary value problem of second order impulsive differential equations

In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.     

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.     

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.