The three-dimensional incompressible magnetohydrodynamic equations with stochastic external forces are considered. First, the existence and uniqueness of local strong solution to the stochastic magnetohydrodynamic equations are proved when the external forces satisfy some conditions. The proof is based on the contraction mapping principle, stopping time and stochastic estimates. The strong solu...

Keywords: Delay dynamic equations Fixed point theory Lyapunov Periodic solutions Stability Time scales a b s t r a c t Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x ∆ (t) = −a(t)x(δ(t))δ ∆ (t). Moreo...

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria unde...

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

We study the two main types of trajectories of the ABC flow in the near-integrable regime: spiral orbits and edge orbits. The former are helical orbits which are perturbations of similar orbits that exist in the integrable regime, while the latter exist only in the non-integrable regime. We prove existence of ballistic (i.e., linearly growing) spiral orbits by using the contraction mapping prin...

In this paper, we deal with a class of BAM neural networks with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of BAM neural networks are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principl...

We examine qualitative properties of solutions of self-consistent Poisson-NernstPlanck (PNP) systems, including uniqueness. In the case of vanishing permanent charge, the predominant case studied, our results unveil a rich structure inherent in these systems, one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes. A particularly significant spec...

*Correspondence: [email protected] 2Department of Applied Mathematics, Central South University, Lushan South Road 932, Changsha, Hunan 410083, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we present some new existence and uniqueness results for nonlinear fractional differential equations with a kind of general irregular boundary co...

Using the contraction principle, in this paper we derive a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reeection mapping. Using these properties, we show that the exponential decay rates of the steady state queue length distributions in an intree network with routing can be derived by a set of recursive equations. The solu...