ON GLOBAL MEROMORPHIC SOLUTIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.

Criteria for System of Three Second-Order Ordinary Differential Equations to Be Reduced to a Linear System via Restricted Class of Point Transformation

This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.

A HIGH ACCURACY DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.

Oscillation Result for Some Non-homogeneous Linear Differential Equations and Its Application

This paper investigates solutions of some non-homogeneous linear differential equations, which have non-homogeneous term as the small function of solution. Using the similar method, we can generalize the result of G.Gundersen and L.Z.Yang.

SOME OSCILLATION THEOREMS OF HIGHER ORDER NON－HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPIC COEFFICIENTS

In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise estimates of the exponent of convergence of the zero sequence of meromorphic solutions for the above equation.

THE COMPLEX OSCILLATION OF NON－HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH INFINITE ORDER ENTIRE COEFFICIENTS

In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.

Entire Solutions of Differential Equations with Finite Order Transcendental Entire Coefficients

In this paper, we investigate the complex oscillation of the differential equation fk+Ak-1fk-1+…+AOf=F where Ak-1.…, Ao F 0 are finite order transcendental entire functions, such that there exists an Ad（0≤d≤k-1） being dominant in the sense that either it has larger order than any other Aj（j=0.…. d-l. d+l.…. k-1）, or it is the only transcendental function. We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation.

GROWTH OF SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH FINITE ORDER ENTIRE COEFFICIENTS

In this paper,we investigate the complex oscillation of some nonhomogeneous equations with finite order transcendental coefficients.Under some conditions we prove that all solutions of these equations are entire functions.Among those solutions, some are of infinite order of growth while some are of finite order of growth.