Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

We define two models of hysteresis that generalize the Preisach model. The first model is deterministic, the second model is stochastic and it utilizes discontinuous transition probabilities that satisfy impulsive differential equations. For the first model we prove, among other things, a local version of the "wiping out" property; for the stochastic model, we give methods for the construction ...

Toxic plants have been used for years in agriculture to control major crop pests. However, the continuous exposure of targeted pests to toxins dramatically increases the rate of resistance evolution (Gassman et al. in Annu Rev Entomol 54:147-163, 2009a; Tabashnik et al. Nat Biotechnol 26:199-202, 2008). To prevent or delay resistance, non toxic host plants can be used as refuges. Our study cons...

It is characteristic for a linear ordinary differential equation that if any solution is bounded on the half-line for any bounded right-hand side then a solution of the corresponding homogeneous equation tends to zero exponentially [1]. The connection of boundedness with exponential behavior of solutions for impulsive differential equations is studied in [2,3] and many other papers. It turns ou...

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and g...

We investigate a class of impulsive gravitational waves which propagate either in Minkowski or in the (anti–) de Sitter background. These waves are constructed as impulsive members of the Kundt class P (Λ) of non-twisting, non-expanding type N solutions of vacuum Einstein equations with a cosmological constant Λ. We show that the only non-trivial waves of this type in Minkowski spacetime are im...

In real world, the ecological systems are usually perturbed by human exploitation activities such as planting and harvesting and so on. In order to obtain a more accurate description for such phenomenon, the impulsive differential equations play an important role. This paper is concerned with a kind of almost periodic Schoener's competition model with pure-delays and impulsive effects. By using...

Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...