• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.699-715
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• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.483-504
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• 2015

This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.217-231
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• 2010

We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• East Asian mathematical journal
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• v.16 no.2
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• pp.251-266
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• 2000

The problem of solution uniqueness to the task of determining unknown parameters of mathematical models from input-output observations is studied. This problem is known as structural identifiability problem. We offer a new approach for testing structural identifiability of linear state space models. The approach compares favorably with numerous methods proposed by other authors for two main reasons. First, it is formulated in obvious mathematical form. Secondly, the method does not involve unfeasible symbolic computations and thus allows to test identifiability of large-scale models. In case of non-identifiability, when there is a set of solutions to the task, we offer a method of computing functions of the unknown parameters which can be determined uniquely from input-output observations and later used as new parameters of the model. Such functions are called parametric functions capable of estimation. To develop the method of computation of these functions we use Lie group transformation theory. Illustrative example is given to demonstrate applicability of presented methods.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.513-530
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• 2021

The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• 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.