An existed abstract result is given,with which we obtained the existence of sign-changing solutions to a class of fourth-order equations boundary value problems.

This paper discusses the existence of positive solutions to two kinds of boundary value problems for a fourth-order equation by using the fixed-point theorem of cone expansion and compression, which are m-point boundary value problem and the integral boudary value problem.

Precise time-integration method for solving four-order rod vibration equation;

In this paper we first consider to establish Hamiltonian systems for four-order rod vibration equation,then use hyperbolic function sinh(x) to construct symplectic schemes in periodic boundary condition with accuracy of arbitrary order.

By applying Hyperbolic function cosh(x), the author constructs a three-level explicit symplectic scheme for four-order rod vibration equation with precision of arbitrary order; and carries out stability analysis.

The paper presents the estimation of the upper bound of generalized second eigenvalue for the differential equation with four orders.

This paper considers a computational method of the approximate value of the generalized eigenvalues of thedifferential equation with four orders and demonstrates the result based on the functional analysis.

This paper studies fourth order diffusion equation with given initial and boundary condi-tion.