Lp theory for semilinear nonlocal problems with measure of noncompactness in separable Banach spaces

被引：13

作者：

Xue, Xingmei ^{[1
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210018, Peoples R China

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2009年 / 5卷 / 01期

关键词：

Nonlocal initial condition; equicontinuous; C-0-semigroup; Hausdorff measure of noncompactness; mild solution; DIFFERENTIAL-EQUATIONS; EVOLUTION-EQUATIONS; CAUCHY-PROBLEMS; INTEGRODIFFERENTIAL EQUATIONS; MILD SOLUTIONS; EXISTENCE; INCLUSIONS; UNIQUENESS;

D O I：

10.1007/s11784-008-0090-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of mild solutions for semilinear differential equations with nonlocal initial conditions in a separable Banach space X. We derive conditions in terms of the Hausdorff measure of noncompactness under which mild solutions exist in L-p(0, b; X). For illustration, a partial integral differential system is worked out.

引用

页码：129 / 144

页数：16

共 50 条

[31] Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations
Yueju Cao
Jitao Sun
Boundary Value Problems, 2016
[32] Nonlinear nonlocal Cauchy problems in Banach spaces
Aizicovici, S
Lee, H
APPLIED MATHEMATICS LETTERS, 2005, 18 (04) : 401 - 407
[33] Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces
Asadollah Aghajani
Ehsan Pourhadi
Juan J. Trujillo
Fractional Calculus and Applied Analysis, 2013, 16 : 962 - 977
[34] Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces
Aghajani, Asadollah
Pourhadi, Ehsan
Trujillo, Juan J.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (04) : 962 - 977
[35] EXISTENCE OF SOLUTIONS FOR SEMILINEAR DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS IN BANACH SPACES
Dong, Qixiang
Li, Gang
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2009, (47)
[36] Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces
Y. K. Chang
J. J. Nieto
W. S. Li
Journal of Optimization Theory and Applications, 2009, 142 : 267 - 273
[37] On Semilinear Integro-Differential Equations with Nonlocal Conditions in Banach Spaces
Tran Dinh Ke
Obukhovskii, Valeri
Wong, Ngai-Ching
Yao, Jen-Chih
ABSTRACT AND APPLIED ANALYSIS, 2012,
[38] Nonresonance problems for differential inclusions in separable Banach spaces
Ding, ZH
Kartsatos, AG
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (08) : 2357 - 2365
[39] Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces
Wang, JinRong
Fan, Zhenbin
Zhou, Yong
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 154 (01) : 292 - 302
[40] Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces
JinRong Wang
Zhenbin Fan
Yong Zhou
Journal of Optimization Theory and Applications, 2012, 154 : 292 - 302

← 1 2 3 4 5 →