• Title, Summary, Keyword: existence and uniqueness

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EXISTENCE AND UNIQUENESS THEOREMS OF SECOND-ORDER EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • Bougoffa, Lazhar;Khanfer, Ammar
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.899-911
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    • 2018
  • In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

UNIQUENESS OF POSITIVE SOLUTIONS FOR PREDATOR-PREY INTERACTING SYSTEMS WITH NONLINEAR DIFFUSION RATES

  • Ahn, Inkyung
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.87-95
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    • 1997
  • In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

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ON SOLVABILITY AND ALGORITHM OF GENERAL STRONGLY NONLINEAR VARIATIONAL-LIKE INEQUALITIES

  • Liu Zeqing;Sun, Juhe;Shim, Soo-Hak;Kang, Shin-Min
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.319-331
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    • 2006
  • In this paper, a new class of general strongly nonlinear variational-like inequalities was introduced and studied. The existence and uniqueness of solutions and a new iterative algorithm for the general strongly nonlinear variational-like inequality are established and suggested, respectively. The convergence criteria of the iterative sequence generated by the iterative algorithm are also given.

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.985-999
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    • 2018
  • This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

AN EXISTENCE AND UNIQUENESS THEOREM OF STOCHASTIC DIFFERENTIAL EQUATIONS AND THE PROPERTIES OF THEIR SOLUTION

  • BAE, MUN-JIN;PARK, CHAN-HO;KIM, YOUNG-HO
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.491-506
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    • 2019
  • In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A KIND OF RAYLEIGH EQUATION WITH A DEVIATING ARGUMENT

  • Zhou, Qiyuan;Xiao, Bing;Yu, Yuehua;Liu, Bingwen;Huang, Lihong
    • Journal of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.673-682
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    • 2007
  • In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Rayleigh equation with a deviating argument of the form $x'+f(x'(t))+g(t,\;x(t-\tau(t)))=p(t)$.

UTILIZING ISOTONE MAPPINGS UNDER MIZOGUCHI-TAKAHASHI CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

  • Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.289-303
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    • 2019
  • We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Mizoguchi-Takahashi 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 integral equation. The results we obtain generalize, extend and unify several very recent related results in the literature.

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)

  • Kim, Mi-Ran;Park, Jong-Seo;Kim, Seon-Yu
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.357-360
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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$\sub$N/$\^$2/ by using the concept of fuzzy number of dimension 2 whose values are normal convex upper semicontinuous and compactly supported surface in R$_2$.

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The existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor

  • Lee, Bu-Young;Kwun, Young-Chel;Ahn, Young-Chel;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.4
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    • pp.339-342
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    • 2009
  • In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

EXISTENCE AND UNIQUENESS THEOREM FOR LINEAR FUZZY DIFFERENTIAL EQUATIONS

  • You, Cuilian;Wang, Gensen
    • East Asian mathematical journal
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    • v.27 no.3
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    • pp.289-297
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    • 2011
  • The introduction of fuzzy differential equation is to deal wit fuzzy dynamic systems. As classical differential equations, it is difficult to find the solutions to all fuzzy differential equations. In this paper an existence and uniqueness theorem for linear fuzzy differential equations is obtained. Moreover, the exact solution to linear fuzzy differential equation is given.