Existence and uniqueness of global solution for abstract second order differential equations with state-dependent delay

被引:8
作者
Hernandez, Eduardo [1 ,2 ]
机构
[1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Comp & Matemat, Sao Paulo, Brazil
[2] Fac Filosofia Ciencias & Letras Ribeirao Preto, Av Bandeirantes 3900, BR-14040901 Ribeirao Preto, SP, Brazil
关键词
abstract Cauchy problem; cosine function; state-dependent delay; C1+ALPHA-STRICT SOLUTIONS; EVOLUTION-EQUATIONS; WELLPOSEDNESS; DYNAMICS;
D O I
10.1002/mana.201900463
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the global existence and uniqueness of solutions and wellposedness of a general class of abstract second order differential equations with state dependent delay. Some examples are presented.
引用
收藏
页码:124 / 139
页数:16
相关论文
共 50 条
  • [1] Existence, uniqueness and approximate controllability of abstract differential equations with state-dependent delay
    Hernandez, Eduardo
    Wu, Jianhong
    Chadha, Alka
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (10) : 8701 - 8735
  • [2] EXISTENCE OF SOLUTIONS FOR A SECOND ORDER ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY
    Hernandez, Eduardo M.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
  • [3] Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
    Karthikeyan, Kulandhivel
    Tamizharasan, Dhatchinamoorthy
    Abdeljawad, Thabet
    Nisar, Kottakkaran Sooppy
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2023, 24 (04) : 1355 - 1368
  • [4] EXISTENCE, UNIQUENESS AND QUALITATIVE PROPERTIES OF GLOBAL SOLUTIONS OF ABSTRACT DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
    Hernandez, Eduardo
    Wu, Jianhong
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019, 62 (03) : 771 - 788
  • [5] Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay
    Hernandez, Eduardo
    Wu, Jianhong
    Fernandes, Denis
    APPLIED MATHEMATICS AND OPTIMIZATION, 2020, 81 (01) : 89 - 111
  • [6] On second order differential equations with state-dependent delay
    Hernandez, Eduardo
    Azevedo, Katia A. G.
    O'Regan, Donal
    APPLICABLE ANALYSIS, 2018, 97 (15) : 2610 - 2617
  • [7] Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay
    Eduardo Hernández
    Jianhong Wu
    Denis Fernandes
    Applied Mathematics & Optimization, 2020, 81 : 89 - 111
  • [8] Existence and uniqueness of solutions, well-posedness and global attractor for abstract differential equations with state-dependent delay
    Hernandez, Eduardo
    Fernandes, Denis
    Wu, Jianhong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 302 : 753 - 806
  • [9] Wellposedness of abstract differential equations with state-dependent delay
    Hernandez, Eduardo
    Azevedo, Katia A. G.
    Rolnik, Vanessa
    MATHEMATISCHE NACHRICHTEN, 2018, 291 (13) : 2045 - 2056
  • [10] Local and Global Existence and Uniqueness of Solution and Local Well-Posednesss for Abstract Fractional Differential Equations with State-Dependent Delay
    Eduardo Hernandez
    Laura R. Gambera
    José Paulo Carvalho dos Santos
    Applied Mathematics & Optimization, 2023, 87