• Title, Summary, Keyword: existence and uniqueness

### Existence and Uniqueness of Solutions for the Fuzzy Differential Equations in n-Dimension Fuzzy Vector Space (n-차원 퍼지벡터공간에서의 퍼지미분방정식에 대한 해의 존재성과 유일성)

• Gwon, Yeong-Cheol;Kim, Oe-Hyeon;Park, Dong-Geun
• Proceedings of the Korean Institute of Intelligent Systems Conference
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• pp.23-25
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• 2008
• In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in ${(E_N)^n}$ using by Banach fixed point theorem. ${(E_N)^n}$ is n-dimension fuzzy vector space.

### Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

• Yang, Wengui
• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.419-430
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• 2016
• In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

### EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR SECOND-ORDER STURM-LIOUVILLE AND MULTI-POINT PROBLEMS ON TIME SCALES

• Sang, Yan-Bin;Wei, Zhongli;Dong, Wei
• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1047-1061
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• 2011
• In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.

### Existence and Uniqueness of Solutions of Fuzzy Integro-Differential equation with Nonlocal condition (비국소 조건을 갖는 퍼지 미분적분방정식의 해의 존재성과 유일성)

• 박동근;한효근;김선유
• Proceedings of the Korean Institute of Intelligent Systems Conference
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• pp.58-63
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• 1998
• We will prove the existence and uniqueness theorem of solutions to the nonlocal fuzzy integro-differential equations using Contraction mapping principle.

### REGULARITY FOR SEMILINEAR RETARDED FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

• Jeong, Jin-Mun;Cheon, Su Jin
• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.559-569
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• 2013
• The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

### THREE-POINT BOUNDARY VALUE PROBLEMS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

• Yang, Wengui
• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012
• In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

### EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATION

• LIANG, BO;WANG, MEISHAN;WANG, YING
• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1059-1068
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• 2015
• The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

### NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION

• FANG ZHONG BO;KWAK, MIN-KYU
• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.829-836
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• 2005
• In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

### Existence and Uniqueness of Solutions for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory

• Kwun, Young-Chel;Park, Jong-Seo;Kim, Seon-Yu;Park, Jin-Han
• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.288-292
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• 2006
• Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

### EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS

• Kim, Yong-In
• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.103-109
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• 2012
• The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$ are investigated, where ${\phi}_p(u)={\mid}u{\mid}^{p-2}u$ with $p$ > 1 and ${\alpha}{\in}C^1$, $e{\in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.