Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations

A class of stochastic differential equations given by dx(t)=f(x(t))dt+g(x(t))dW(t),  x(t0)=x0,  t0≤t≤T<+∞, are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis

Improved Electrochemical Performance of Surface Coated LiNi0.80Co0.15Al0.05O2 With Polypyrrole

Nickel-rich ternary layered oxide (LiNi0.80Co0.15Al0.05O2, LNCA) cathodes are favored in many fields such as electric vehicles due to its high specific capacity, low cost, and stable structure. However, LNCA cathode material still has the disadvantages of low initial coulombic efficiency, rate capability and poor cycle performance, which greatly restricts its commercial application. To overcome this barrier, a polypyrrole (PPy) layer with high electrical conductivity is designed to coat on the surface of LNCA cathode material. PPy coating layer on the surface of LNCA successfully is realized by means of liquid-phase chemical oxidation polymerization method, and which has been verified by the scanning electron microscopy (SEM), transmission electron microscope (TEM) and fourier transform infrared spectroscopy (FTIR). PPy-coated LNCA (PL-2) exhibits satisfactory electrochemical performances including high reversible capacity and excellent rate capability. Furthermore, the capability is superior to pristine LNCA. So, it provides a new structure of conductive polymer modified cathode materials with good property through a mild modification method

On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

We investigate a class of functional integral equations of fractional order given by x(t)=q(t)+f1(t,x(α1(t)),x(α2(t)))+(f2(t,x(β1(t)),x(β2(t)))/Γ(α))×∫0t(t−s)α−1f3(t,s,x(γ1(s)), x(γ2(s)))ds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived. The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage. Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals. Moreover, two examples are given to illustrate our results

Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

In this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area

Periodic Measures of Mean-Field Stochastic Predator-Prey System

This paper discusses the dynamics of the mean-field stochastic predator-prey system. We prove the existence and pathwise uniqueness of the solution for stochastic predator-prey systems in the mean-field limit. Then we show that the solution of the mean-field equation is a periodic measure. Finally, we study the fluctuations of the periodic in distribution processes when the white noise converges to zero