• Title/Summary/Keyword: existence of solution

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UNIFORM DECAY OF SOLUTIONS FOR VISCOELASTIC PROBLEMS

  • Bae, Jeong-Ja
    • East Asian mathematical journal
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    • v.19 no.2
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    • pp.189-205
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    • 2003
  • In this paper we prove the existence of solution and uniform decay rates of the energy to viscoelastic problems with nonlinear boundary damping term. To obtain the existence of solutions, we use Faedo-Galerkin's approximation, and also to show the uniform stabilization we use the perturbed energy method.

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CONVERGENCE OF EXPONENTIALLY BOUNDED C-SEMIGROUPS

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • v.9 no.2
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    • pp.115-121
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    • 2001
  • In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

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DIRICHLET BOUNDARY VALUE PROBLEM FOR A CLASS OF THE NONCOOPERATIVE ELLIPTIC SYSTEM

  • JUNG, TACKSUN;CHOI, Q-HEUNG
    • Korean Journal of Mathematics
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    • v.23 no.2
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    • pp.259-267
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    • 2015
  • This paper is devoted to investigate the existence of the solutions for a class of the noncooperative elliptic system involving critical Sobolev exponents. We show the existence of the negative solution for the problem. We show the existence of the unique negative solution for the system of the linear part of the problem under some conditions, which is also the negative solution of the nonlinear problem. We also consider the eigenvalue problem of the matrix.

MOMENT ESTIMATE AND EXISTENCE FOR THE SOLUTION OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION

  • Chen, Huabin;Wan, Qunjia
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.279-298
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    • 2022
  • In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.

EXISTENCE AND UNIQUENESS OF A SOLUTION FOR FIRST ORDER NONLINEAR LIOUVILLE-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

  • Nanware, J.A.;Gadsing, Madhuri N.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.1011-1020
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    • 2021
  • In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH A SINGULAR WEIGHT

  • Jeongmi Jeong;Yong-Hoon Lee
    • East Asian mathematical journal
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    • v.40 no.1
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    • pp.51-61
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    • 2024
  • In this work, we study the existence of a positive solution for nonlinear fractional differential equation with a singular weight. For the proof, we introduce newly defined solution operator and use well-known Krasnoselski's fixed point theorem. We also give an example with a singular weight which may not be integrable.

PERIODIC SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS TO LOGISTIC EQUATION AND NEURAL NETWORKS

  • Li, Dingshi;Xu, Daoyi
    • Journal of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1165-1181
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    • 2013
  • In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].

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.