• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.597-610
• /
• 2024

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.597-607
• /
• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.265-277
• /
• 2004

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.797-803
• /
• 2020

The Brück conjecture is still open for an entire function f with hyper order of no less than 1/2, which is not an integer. In this paper, it is proved that the hyper order of solutions of a linear complex differential equation that is related to the Brüuck Conjecture is infinite. The results show that the conjecture holds in a special case when the hyper order of f is 1/2.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.425-441
• /
• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.295-309
• /
• 2020

In this paper we study the growth of solutions of some non-linear complex differential equations in connection to Brück conjecture using the theory of complex differential equation.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.473-481
• /
• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.507-513
• /
• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.2
• /
• pp.303-322
• /
• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1495-1506
• /
• 2021

The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.