• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.513-534
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• 2024

The main goal of this work is to study an initial boundary value problem relating to the unsteady flow of a rigid, viscoplastic, and incompressible Bingham fluid in an elastic bounded domain of ℝ². By using the approximation sequences of the Faedo-Galerkin method together with the regularization techniques, we obtain the results of the existence and uniqueness of local solutions.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.325-338
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• 1998

Some nonlocal boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of the solutions. We consider the Dirichlet type boundary value problem and the Neumann type boundary value problem with nonlinear boundary conditions. We also provide a regularity results for the solutions.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.169-190
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• 2008

Second-order parabolic equations with variable coefficients are considered on $\mathbb{R}^d$ and $C^1$ domains. Existence and uniqueness results are given in $L_q(L_p)$-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.867-885
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• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.363-370
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• 2005

In this paper, we obtain a new fixed point theorem in complete probabilistic ${\Delta}$-inner product space. As an example of applications, we utilize the results of this paper to study the existence and uniqueness of solutions for linear Valterra integral equation.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.153-169
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• 2005

A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1441-1450
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• 2013

In this paper, we consider two-component Bose-Einstein condensates with an internal atomic Josephson junction in the general case, i.e., 0 < p < $\frac{2}{(d-2)^+}$. We prove existence and uniqueness results for the ground states, and obtain some properties of the ground states with large parameters.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.627-639
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• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.39-52
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• 2022

We introduce Clifford-valued neural networks with leakage delays. Furthermore, we study the uniqueness and existence of Clifford-valued Hopfield artificial neural networks having the Stepanov weighted pseudo almost periodic forcing terms on leakage delay terms. However the noncommutativity of the Clifford numbers' multiplication made our investigation diffcult, so our results are obtained by decomposing Clifford-valued neural networks into real-valued neural networks. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.