The principle of least action with variables was used to solve the forced vibration of the rectangular plate with three clamped and the other free under concentrated load,and the corresponding stable solution was obtained.

In this paper,we give out two exist and unique criterias of stable solution for second order Hopfield neural network with reaction and diffusion utilizing the principle of compression.

In this paper,the method of mixed variables is applied to the problems of forced vibration of the rectangular plate under uniform load,the stable solution of the plate with three sides clamped and the other free under uniform load can be worked out.

In order to better understand the mechanical behavior of railway vehicles from a straight track into a curved track, the steady-state solutions(equilibrium p oints) of a vehicle system are investigated.

The relationship between the time-dependent solution and steady-state solution is considered,a decay estimate between the time-dependent solution and steady-state solution is given by series of estimate on the solution under some conditions.

This paper,beginning with the general age-dependent population dynamics,discusses the well-pose of stationary solution.

It can be produced by the evolution of a stationary solution of nonlinear Schrdinger equation with a periodic potential modulation.

Then, the stationary solution of the dynamic equations governing an active Brownian particle moving in a plane with Schienbein-Gruler velocity-dependent friction model subject to Guassian white noise excitation is obtained by using this method.

It is explained when the total population is not a constant,the constant positive steady solution of the reaction-diffusion equations is asymptotical stability,therefore the Turing bifurcations do not exist.

In this paper, we discussed the existence and asymptotic behaviors of steady solutions for some kinds of reaction diffusion equations with time delays.

Firstly,the steady solution of Oldroyd-B model is given in the paper.