• Title/Summary/Keyword: Nonlocal condition

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ASYMPTOTIC STABILITY OF STRONG SOLUTIONS FOR EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

  • Chen, Pengyu;Kong, Yibo;Li, Yongxiang
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.319-330
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    • 2018
  • This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.

EXISTENCE FOR A NONLINEAR IMPULSIVE FUNCTIONAL INTEGRODIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS IN BANACH SPACES

  • Yan, Zuomao
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.681-696
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    • 2011
  • In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

BLOW UP OF SOLUTIONS WITH POSITIVE INITIAL ENERGY FOR THE NONLOCAL SEMILINEAR HEAT EQUATION

  • Fang, Zhong Bo;Sun, Lu
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.16 no.4
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    • pp.235-242
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    • 2012
  • In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

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 the 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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EXISTENCE OF INFINITELY MANY SOLUTIONS FOR A CLASS OF NONLOCAL PROBLEMS WITH DIRICHLET BOUNDARY CONDITION

  • Chaharlang, Moloud Makvand;Razani, Abdolrahman
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.155-167
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    • 2019
  • In this article we are concerned with some non-local problems of Kirchhoff type with Dirichlet boundary condition in Orlicz-Sobolev spaces. A result of the existence of infinitely many solutions is established using variational methods and Ricceri's critical points principle modified by Bonanno.

Controllability for the Nonlinear Fuzzy Control System with Nonlocal Initial Condition in EnN

  • Lee, Bu-Young;Park, Dong-Gun;Choi, Gyu-Tak;Kwun, Young-Chel
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.6 no.1
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    • pp.15-20
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    • 2006
  • In this paper we study the exact controllability for the nonlinear fuzzy control system with nonlocal initial condition in $E_N^n$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in $R^n$. $E_N^n$ be the set of all fuzzy numbers in $R^n$ with edges having bases parallel to axis $X_1,X_2,\;,X_n$.