New comparison results for impulsive functional differential equations

AbstractComparison principles play an important role in the qualitative and quantitative study of differential equations. In this paper, we establish new maximum principles for impulsive functional differential equations

ON HIGHER ORDER NONLINEAR IMPULSIVE BOUNDARY VALUE PROBLEMS

This work studies some two point impulsive boundary value problems composed by a fully differential equation, which higher order contains an increasing homeomorphism, by two point boundary conditions and impulsive e ects. We point out that the impulsive conditions are given via multivariate generalized functions, including impulses on the referred homeomorphism. The method used apply lower and upper solutions technique together with xed point theory. Therefore we have not only the existence of solutions but also the localization and qualitative data on their behavior. Moreover a Nagumo condition will play a key role in the arguments

Critical point approaches to second-order differential systems generated by impulses

Using variational methods and critical point theory, we establish multiplicity results of solutions for second-order differential systems generated by impulses. Indeed, employing two sorts of three critical points theorems, we establish the multiplicity results for weak solutions of the problem and verify that these solutions are generated by impulses.Publisher's Versio

Multiple solutions for a class of perturbed second-order differential equations with impulses

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On the Existence of Solutions for Impulsive Duffing Dynamic Equations on Time Scales with Dirichlet Boundary Conditions

By using critical point theory, some new sufficient conditions for the existence of solutions of impulsive Duffing dynamic equations on time scales with Dirichlet boundary conditions are obtained. Some examples are also given to illustrate our results

Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained

A Class of Impulsive Pulse-Width Sampler Systems and Its Steady-State Control in Infinite Dimensional Spaces

This paper investigates a class of impulsive pulse-width sampler systems and its steadystate control in the infinite dimensional spaces. Firstly, some definitions of pulse-width sampler systems with impulses are introduced. Then applying impulsive evolution operator and fixed point theorem, some existent results of steady-state of infinite dimensional linear and semilinear pulse-width sampler systems with impulses are obtained. An example to illustrate the theory is presented in the end

Existence results on positive periodic solutions for impulsive functional differential equations

A class of first order nonlinear functional differential equations with impulses is studied. It is shown that there exist one or two positive T-periodic solutions under certain assumptions, and no positive T-periodic solution under some other assumptions. Applications to some impulsive biological models and an example, which can not be covered by known results, are given to illustrate the main results