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

页数：8

共 50 条

[21] Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
Chung-Sik Sin
Hyok-Chol In
Kwang-Chol Kim
[J]. Advances in Difference Equations, 2018
[22] Existence of mild solutions for impulsive fractional evolution equations with periodic boundary conditions
Gou, Haide
Li, Yongxiang
[J]. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2020, 11 (01) : 425 - 445
[23] The existence of solutions for nonlinear impulsive evolution equations
Zhang, LL
Wang, WX
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2006, 13 : 593 - 600
[24] General theorems on the existence and uniqueness of solutions of impulsive differential equations
Slyusarchuk V.E.
[J]. Ukrainian Mathematical Journal, 2000, 52 (7) : 1094 - 1106
[25] Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations
Liu, Zhenhai
Li, Xiuwen
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (06) : 1362 - 1373
[26] Existence of Mild and Classical Solutions for Nonlocal Impulsive Integrodifferential Equations in Banach Spaces with Measure of Noncompactness
Karthikeyan, K.
Anguraj, A.
Malar, K.
Trujillo, Juan J.
[J]. INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 2014
[27] Existence and uniqueness of positive mild solutions for a class of fractional evolution equations on infinite interval
Yi Chen
Zhanmei Lv
Liang Zhang
[J]. Boundary Value Problems, 2017
[28] Existence uniqueness of mild solutions for ψ-Caputo fractional stochastic evolution equations driven by fBm
Min Yang
[J]. Journal of Inequalities and Applications, 2021
[29] Existence Results of Mild Solutions for Impulsive Fractional Integrodifferential Evolution Equations With Nonlocal Conditions
Zhang, Xuping
Gou, Haide
Li, Yongxiang
[J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2019, 20 (01) : 1 - 16
[30] Existence and uniqueness of positive mild solutions for a class of fractional evolution equations on infinite interval
Chen, Yi
Lv, Zhanmei
Zhang, Liang
[J]. BOUNDARY VALUE PROBLEMS, 2017,

← 1 2 3 4 5 →