• International Journal of Fuzzy Logic and Intelligent Systems
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• 제4권1호
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• pp.40-44
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• 2004

In this paper we study the existence and uniqueness of fuzzy solutions for the nonlinear fuzzy integro-differential equations on $E^{n}_{N}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in $E^{n}_{N}$. $E^{n}_{N}$ be the set of all fuzzy numbers in $R^{n}$ with edges having bases parallel to axis $x_1$, $x_2$, …, $x_n$.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.49-64
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• 2024

When setting up a structure with an embedded shallow arch, there is a phenomenon where the end of the arch moves. To study the so-called moving domain problem, one try to transform a considered noncylindrical domain into the cylindrical domain using the transform operator, as well as utilizing the method of penalty and other approaches. However, challenges arise when calculating time derivatives of solutions in a domain depending on time, or when extending the initial conditions from the non-cylindrical domain to the cylindrical domain. In this paper, we employ the transform operator to prove the existence and uniqueness of weak solutions of the shallow arch equation on the moving domain as clarifying the time derivatives of solutions in the moving domain.

• Korean Journal of Mathematics
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• 제12권1호
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• pp.77-90
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• 2004

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system of the Dirichlet problem on the bounded domain ${\Omega}$ in $R^n$. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.35-50
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• 2007

In this work, optimal harvesting policy for the predator-prey system of three species with age-dependent and diffusion is discussed. Existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.587-601
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• 2011

In this paper, we prove the existence and uniqueness of mild solution for stochastic functional integrodifferential evolution equations and derive sufficient conditions for the controllability results. As an illustration we consider the controllability for a system governed by a random motion of a string.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.545-558
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• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• 대한수학회지
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• 제55권1호
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• pp.73-82
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• 2018

In this article we consider certain types of nonlinear matrix equations including the stochastic rational Riccati equation and show the existence and uniqueness of the positive definite solution by using Bhaskar-Lakshmikantham's coupled fixed point theorem.

• 호남수학학술지
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• 제35권4호
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• pp.679-681
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• 2013

In this paper, we raise a question regarding existence and uniqueness of the steady-state solution of a type of Kolmogorov forward equation. We prove that the question has a positive answer for trivial vector fields, and also provide examples which show that the compactness assumption is necessary.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1037-1048
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• 2008

The purpose of this paper is to present a differential equation with delay from biological excitable medium. Existence, uniqueness and data dependence (monotony, continuity, differentiability with respect to parameter) results for the solution of the Cauchy problem of biological excitable medium are obtained using weakly Picard operator theory.

• 충청수학회지
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• 제29권2호
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.