MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.

ON ZEROS OF SOLUTIONS OF HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS

In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak-1 is the dominant coefficient, then every transcendental solution f（z） of equation……satisfies ）λ（f） =∞, where A（f） denotes the exponent of convergence of zeros of the meromor- phic function f（z）.

On the Location of Zeros of Higher Order Differential Equation

In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order differential equation, which can be regarded as an alternating but precise version of Wu and Yi.

SECTORIAL OSCILLATION THEORY OF LINEAR DIFFERENTIAL EQUATIONS

In this paper, the sectorial oscillation of the solutions of higher order homo- geneous linear differential equationswith infinite order entire function coefficients is studied. Results are obtained to extend some results in [19] and [18].

Growth of Solutions of Some Linear Difference Equations with Meromorphic Coefficients

In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.

Complex oscillation of certain high non-homogeneous linear differential equations

This present paper investigates the complex oscillation theory of certain high non-homogeneous linear differential equations and obtains a series of new results.

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.

Estimates for the zeros of differences of meromorphic functions

Let f be a transcendental meromorphic function and g(z)=f(z+c1)+f(z+c2)-2f(z) and g2(z)=f(z+c1)·f(z+c2)-f2(z).The exponents of convergence of zeros of differences g(z),g2(z),g(z)/f(z),and g2(z)/f2(z) are estimated accurately.

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.

OSCILLATION THEORY TO SOME COMPLEX LINEAR LARGE DIFFERENTIAL EQUATIONS

In this paper, some complex linear differential equations are investigated. Many results on the relation between solutions and their derivatives are obtained.