• Title, Summary, Keyword: existence and uniqueness

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THE EXISTENCE, NONEXISTENCE AND UNIQUENESS OF GLOBAL POSITIVE COEXISTENCE OF A NONLINEAR ELLIPTIC BIOLOGICAL INTERACTING MODEL

  • Kang, Joon Hyuk;Lee, Jungho;Oh, Yun Myung
    • Korean Journal of Mathematics
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    • v.12 no.1
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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.

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A FOURTH-ORDER ACCURATE FINITE DIFFERENCE SCHEME FOR THE EXTENDED-FISHER-KOLMOGOROV EQUATION

  • Kadri, Tlili;Omrani, Khaled
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.297-310
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    • 2018
  • In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

The existence and uniqueness of solution for the nonlinear fuzzy differential equations with nonlocal initial condition (비국소 초기 조건을 갖는 비선형 퍼지 미분방정식에 대한 해의 존재성과 유일성)

  • 박종서;김선유;강점란;권영철
    • Journal of Korean Institute of Intelligent Systems
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    • v.11 no.8
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    • pp.715-719
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    • 2001
  • In this paper, we study the existence and uniqueness of fuzzy solution for the nonlinear fuzzy differential equations with nonlocal initial condition in E$^{2}$$_{N}$

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Singular solutions of semilinear parabolic equations

  • Baek, Geong-Seon;Kwak, Min-Kyu
    • Journal of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.483-492
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    • 1995
  • In this paper we discuss the existence and uniqueness of singular solutions for equations of the form $$ (F) u_t = u{xx} - $\mid$u$\mid$^{q-1} u_x - $\mid$u$\mid$^{p-1}u, p,q > 1, $$ in the domain $Q = {(x,t) : x \in R, t > 0}$. This equation represents a model of diffusion-convection with absorption.

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THREE POINT BOUNDARY VALUE PROBLEMS FOR THIRD ORDER FUZZY DIFFERENTIAL EQUATIONS

  • Murty, M.S.N.;Kumar, G. Suresh
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.1
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    • pp.101-110
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    • 2006
  • In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

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A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS

  • Lan, Heng-You
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.111-123
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    • 2008
  • In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

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ON THE EXISTENCE OF SOLUTIONS OF QUASILINEAR WAVE EQUATIONS WITH VISCOSITY

  • Park, Jong-Yeoul;Bae, Jeong-Ja
    • Journal of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.339-358
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    • 2000
  • Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .

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