In this paper, we study mixed boundary value problem for secondorder impulsive differential equations with a parameter. By using critical point theory, several new existence results are obtained. This is one of the first times that impulsive boundary value problems are studied by means of variational methods.

In this paper, a prey predator impulsive mathematical model of integrated pest management is established, in which infected prey and predator (natural enemy) are released impulsively. By using the Floquet’s theory for impulsive differential equations, small-amplitude perturbation methods and comparison techniques, we investigate the local and global stability of the susceptible pest-eradication...

In this paper, we study the existence and uniqueness of mild solutions for random impulsive differential equations through fixed point technique. An example is provided to illustrate theory.

In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with “non-periodic” boundary conditions. These boundary conditions include, as a special case, so-called “anti-periodic” boundary conditions. Our methods to prove the existence and uniqueness of solutions involve new differential ine...

This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.

In this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By using the Floquet theory for impulsive differential equations, we show that there exists a globally asymp...

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H 2 ð1=2; 1Þ in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coeffici...

The method of averaging is applied to study the existence solutions boundary value problems for systems differential equations with non-fixed moments impulse action. It shown that if an averaged problem has a solution, then original solvable as well. Here impulsive system simpler ordinary equations.

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of ...