• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.111-113
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• 1997

A simple proof for the special case of the McMillan and Pommerenke Theorem on the asymptotic values of meromorphic functions without Koebe arcs is derived from the author's result on the boundary behavior of meromorphic functions without Koebe arcs.

• East Asian mathematical journal
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• v.40 no.1
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1143-1155
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• 2011

In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.355-365
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• 2014

We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.17-28
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• 2017

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.499-512
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• 2011

The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its ${\kappa}$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br$\"{u}$-ck conjecture with the idea of sharing polynomial.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.107-122
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• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.679-689
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• 2022

In this paper, we establish sufficient conditions for the existence and uniqueness of solution for a class of initial boundary value problems with Dirichlet condition in regard to a category of fractional-order partial differential equations. The results are established by a method based on the theorem of Lax Milligram.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.475-484
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• 2015

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If fⁿ(f³ - 1)f′ and gⁿ(g³ - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).