• Title, Summary, Keyword: existence and uniqueness

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LOCAL EXISTENCE AND GLOBAL UNIQUENESS IN ONE DIMENSIONAL NONLINEAR HYPERBOLIC INVERSE PROBLEMS

  • Choi, Jong-Sung
    • Communications of the Korean Mathematical Society
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    • v.17 no.4
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    • pp.593-606
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    • 2002
  • We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

EXISTENCE-AND-UNIQUENESS AND MEAN-SQUARE BOUNDEDNESS OF THE SOLUTION TO STOCHASTIC CONTROL SYSTEMS

  • Lu, Peilin;Cao, Caixia
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.513-522
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    • 2013
  • This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

EXISTENCE, UNIQUENESS AND STABILITY OF IMPULSIVE STOCHASTIC PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

  • Anguraj, A.;Vinodkumar, A.
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.739-751
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    • 2010
  • This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

EXISTENCE AND UNIQUENESS OF ENDEMIC STATES FOR AN EPIDEMIC MODEL WITH EXTERNAL FORCE OF INFECTION

  • Cha, Young-Joon
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.175-187
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    • 2002
  • The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.

Global Existence and Ulam-Hyers Stability of Ψ-Hilfer Fractional Differential Equations

  • Kucche, Kishor Deoman;Kharade, Jyoti Pramod
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.647-671
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    • 2020
  • In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

Existence and Uniqueness of Solutions of Fractional Differential Equations with Deviating Arguments under Integral Boundary Conditions

  • Dhaigude, Dnyanoba;Rizqan, Bakr
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.191-202
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    • 2019
  • The aim of this paper is to develop a monotone iterative technique by introducing upper and lower solutions to Riemann-Liouville fractional differential equations with deviating arguments and integral boundary conditions. As an application of this technique, existence and uniqueness results are obtained.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR SINGULAR THREE-POINT BOUNDARY VALUE PROBLEMS

  • Miao, Chunmei;Ge, Weigao
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.895-902
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    • 2009
  • In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SINGULAR SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • Wang, Lin;Lu, Xinyi
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.877-894
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    • 2013
  • In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.