EKELAND'S VARIATIONAL PRINCIPLE AND CARISTI'S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE

The main purpose of this paper is to establish the Ekeland’s variational principle andCaristi’s fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these two theorems in the probabilistic metric space. The resultspresented in this paper generalize the corresponding results of [9--12].

Oscillation in a Class of Neutral Differential Equations with Positive and Negative Coefficients

The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.

A Boundary Value Problem for Second Order Functional Differential Equations with Impulses

Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results of the esistence, the uniqueness and the continuous dependence on aprameter of soiutions of the boundary value problems for second order functional differential equations with impulses are obtained.

Bessel算子的非线性扰动

对于非线性Sturm——Liouvitte问题,近年来有不少研究工作,并得到了许多好的结果。例如常型的见[1],奇型的见[4],且可用于孤子的研究。本文研究一端带奇型的有界区间上的非线性特征值问题: Ly=-(d/(dx))[x((dy)/(dx))]+[m^2/x-q(x,y,y′)]=λxy。 y(x)∈L_2(o,a),(a>o)。 (1) 其中m≥2,q(x,y,y′)∈[o,a]×R×R上的实连续函数,q(x,y,y′)/x有界。当(1)中g≡o时,它可产生Bessee函数。且(?)+g(x,y,y′)/x]存在。

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of kth-order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature.

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.

Global Attracting Sets of Neutral Stochastic Functional Differential Equations Driven by Poisson Jumps

By means of the Banach fixed point principle,we establish some sufficient conditions ensuring the existence of the global attracting sets and the exponential decay in the mean square of mild solutions for a class of neutral stochastic functional differential equations by Poisson jumps.An example is presented to illustrate the effectiveness of the obtained result.