EXISTENCE AND UNIQUENESS OF MILD AND CLASSICAL SOLUTIONS OF IMPULSIVE EVOLUTION EQUATIONS

被引：0
|
作者：
Anguraj, Annamalai [1 ]
Arjunan, Mani Mallika [1 ]
机构：
[1] PSG Coll Arts & Sci, Dept Math, Coimbatore 641014, Tamil Nadu, India
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2005年
关键词：
Semigroups; evolution equations; impulsive conditions;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the non- linear impulsive evolution equation u'(t) = Au(t) + f(t, u(t), Tu(t), Su(t)), 0 < t < T0, t 6 = ti, u(0) = u0, Delta u(t(i)) = I-i(u(t(i))), i = 1, 2, 3,..., p. in a Banach space X, where A is the infinitesimal generator of a C-0 semigroup. We study the existence and uniqueness of the mild solutions of the evolution equation by using semigroup theory and then show that the mild solutions give rise to a classical solutions.
引用
收藏
页数：8
相关论文
共 50 条
  • [1] Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
    Shah, Vishant
    George, Raju K.
    Sharma, Mita
    Muthukumar, P.
    [J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2018, 19 (7-8) : 775 - 780
  • [2] Existence and uniqueness of mild solutions to impulsive fractional differential equations
    Mophou, Gisele M.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1604 - 1615
  • [3] Existence and uniqueness of positive mild solutions for nonlocal evolution equations
    Chen, Pengyu
    Li, Yongxiang
    Zhang, Xuping
    [J]. POSITIVITY, 2015, 19 (04) : 927 - 939
  • [4] Existence and uniqueness of positive mild solutions for nonlocal evolution equations
    Pengyu Chen
    Yongxiang Li
    Xuping Zhang
    [J]. Positivity, 2015, 19 : 927 - 939
  • [5] Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations
    Pallavi Bedi
    Anoop Kumar
    Thabet Abdeljawad
    Aziz Khan
    [J]. Advances in Difference Equations, 2020
  • [6] Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations
    Bedi, Pallavi
    Kumar, Anoop
    Abdeljawad, Thabet
    Khan, Aziz
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [7] The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay
    Zhang, Xianmin
    Huang, Xiyue
    Liu, Zuohua
    [J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (04) : 775 - 781
  • [8] Existence and uniqueness of solutions for impulsive fractional differential equations
    Rehman, Mujeeb Ur
    Eloe, Paul W.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 422 - 431
  • [9] EXISTENCE AND UNIQUENESS OF SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS
    Benchohra, Mouffak
    Slimani, Boualem Attou
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2009,
  • [10] EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR STOCHASTIC IMPULSIVE DIFFERENTIAL EQUATIONS
    Shen, Lijuan
    Sun, Jitao
    [J]. STOCHASTICS AND DYNAMICS, 2010, 10 (03) : 375 - 383
12345