Existence of solutions for second order impulsive differential equations with deviating arguments

This paper deals with impulsive second order differential equations with deviating arguments. We investigate the existence of solutions of such problems with nonlinear boundary conditions. To obtain corresponding results we discuss also second order impulsive differential inequalities with deviating arguments.     

Periodic boundary value problems for second-order impulsive integro-differential equations

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second-order nonlinear impulsive integro-differential equations of mixed type.     

Periodic boundary value problems of second-order impulsive differential equations

This paper discusses periodic boundary value problems of second-order impulsive differential equations. By using Schaeffer’s fixed-point theorem and monotone iterative technique, some existence results are obtained.     

Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces

This paper investigates the existence of solutions for a class of second-order boundary-value problems with integral boundary conditions of nonlinear impulsive integro-differential equations in Banach spaces. The arguments are based upon the fixed point theorem of strict set contraction operators. Meanwhile, an example is worked out to demonstrate the main results.     

Variational methods to Sturm-Liouville boundary value problem for impulsive differential equations

In this paper, we study a linear Sturm-Liouville impulsive problem and a nonlinear Sturm-Liouville impulsive problem. By applying a new approach via critical point theory and variational methods, the existence results of positive solutions are obtained.     

Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions

In this paper, the existence of at least three positive solutions to impulsive second order differential equations is investigated. Sufficient conditions which guarantee the existence of positive solutions are obtained, by using the Avery-Peterson theorem. An example is added to illustrate the results.     

Nagumo type existence results of Sturm-Liouville BVP for impulsive differential equations

In this paper, the method of upper and lower solutions and the Schauder degree theory are employed in the study of Sturm-Liouville boundary value problems for second order impulsive differential equations. We obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a Nagumo condition with respect to the first order derivative.     

Second order singular boundary value problems with integral boundary conditions

We study the second order singular boundary value problem

     

Boundary value problems for first order differential equations of mixed type

We apply the monotone iterative method to formulate existence results for integro-differential equations with nonlinear boundary conditions. Some results for integro-differential inequalities are also given. Examples illustrate obtained results.     

Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations

In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed‐point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.     

Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions

This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand.     

Subharmonic solutions with prescribed minimal period for some second-order impulsive differential equations

This paper uses critical point theory and variational methods to investigate the subharmonic solutions with prescribed minimal period for a class of second-order impulsive differential equations. The conditions for the existence of subharmonic solutions are established. Our results rectify some known results in the literature and will allow us, in the future, to deal with the subharmonic solutions for more extensive impulsive problems.     

Second-order boundary value problems with integral boundary conditions

In this paper we investigate the existence of positive solutions of nonlocal second-order boundary value problems with integral boundary conditions.     

Solution tube method for impulsive periodic differential inclusions of first order

The aim of this paper is to obtain an existence result for impulsive differential inclusions of first order with boundary conditions in Hilbert spaces under a hypothesis of integrability in the Henstock-Lebesgue sense for the multifunction on the right-hand side. The proof is based on the assumption that there exists a solution tube for the inclusion taken under consideration (this novel concept which generalizes the extensively used notions of upper and lower solution was adapted to the present setting). Finally, a compactness property is proved.     

Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions

The existence, uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal Cauchy problem in general Banach spaces are studied, by using the fixed point technique and semigroup of operators.     

General methods for converting impulsive fractional differential equations to integral equations and applications

In this paper, we propose the concepts of Caputo fractional derivatives and Caputo type Hadamard fractional derivatives for piecewise continuous functions. We obtain general solutions of four classes of impulsive fractional differential equations (Theorem 3.1–Theorem 3.4) respectively. These results are applied to converting boundary value problems for impulsive fractional differential equations to integral equations. Some comments are made on recently published papers (see Section 4).     

Boundary value problems for first order impulsive delay differential equations with a parameter

In this paper, by means of the method of upper and lower solutions and monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established.