Existence of solutions for a class of fourth-order difference boundary value problem and critical point method;

Positive solutions of boundary value problems for systems of nonlinear fourth-order differential equations;

The existence of at least two positive solutions is proved for the nonlinear fourth-order periodic boundary valve problem u(4)(t)-βu″(t)+αu(t)=λf(t,u(t)),0≤t≤1,u(i)(0)=u(i)(1),i=0,1,2,3,where β>-2π2,0<α<(1/2β+2π2)2,α/π4+β/π2+1>0,λ>0 is a constant and f:×[0,+∞)→[0,+∞) is continuous by using fixed-point theorem and degree theory.

The solvable condition of the fourth order variable coefficient linear differential equations;

We study the existence of positive solutions of fourth order semipositive boundary value problem y (4) -λf(x,y)=0,0<x<1 y(0)=y(1)=y′(0)=y′(1)=0 where λ>0, the main methods are fixed point theorems in a cone.

The theorem that a kind of fourth order linear differential equation with variable coefficients can be changed into fourth order linear differential equations with constant coefficients is deduced.

By means of variable substitution and complex functional derivation method,this paper gives a new kind of four order different equation,some kind of solution with sufficient and necesiory conditions.

By means of dual variation method and deviation method,this paper gives one kind of four order nonlinear differential equation and sufficient conditions for some kind of solutions.

Not only mulitiparticles term neglected in general work is considered but also four order terms.

Aiming at the disadvantages of traditional prediction methods in railway passenger volume,a joint application of improved BP neural network and four-stage method in passenger volume prediction is brought out.

This paper analyzes the characteristics of highway construction project,then discusses the traffic forecasting method using four-stage method in highway construction project on the basis of area economic development forecasting.

The number was calculated by four-stage method.