On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions

被引：3

作者：

Cao, Nan ^{[1
]}

Fu, Xianlong ^{[2
,3
]}

机构：

[1] Shanghai Dianji Univ, Sch Arts & Sci, Shanghai 201306, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Key Lab, MEA Minist Educ, Shanghai 200241, Peoples R China

[3] East China Normal Univ, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2023年 / 26卷 / 05期

关键词：

Neutral integro-differential equation; Nonlocal condition; Approximate controllability; Resolvent operator; Fundamental solution; RESOLVENT OPERATORS; INTEGRAL-EQUATIONS; EXISTENCE; DELAY;

D O I：

10.1007/s13540-023-00185-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the approximate controllability of a class of semi-linear neutral integro-differential equation with nonlocal condition. The basic tools of this study are the theory of resolvent operators of linear neutral integro-differential equation and fractional powers. The fundamental solution of linear neutral integro-differential equations is also constructed to deal with the non-uniform boundedness of the extra linear term. Sufficient conditions of approximate controllability are then obtained through the resolvent condition. Finally, an example is provided to illustrate the applications of the obtained results.

引用

页码：2237 / 2263

页数：27

共 40 条

[1] On concepts of controllability for deterministic and stochastic systems [J].

Bashirov, AE ;

Mahmudov, NI .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) :1808-1821

[2] THEOREMS ABOUT THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF A SEMILINEAR EVOLUTION NONLOCAL CAUCHY-PROBLEM [J].

BYSZEWSKI, L .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 162 (02) :494-505

[3] Global solutions of abstract semilinear parabolic equations with memory terms [J].

Cannarsa, P ;

Sforza, D .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2003, 10 (04) :399-430

[4] ON NON-LOCAL PROBLEMS FOR PARABOLIC EQUATIONS [J].

CHABROWSKI, J .

NAGOYA MATHEMATICAL JOURNAL, 1984, 93 (MAR) :109-131

[5]

Curtain R, 1995, INTRO INFINITE DIMEN, DOI DOI 10.1007/978-1-4612-4224-6

[6] EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY [J].

Dos Santos, Jose Paulo C. ;

Henriquez, Hernan ;

Hernandez, Eduardo .

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2011, 23 (02) :289-330

[7] Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces [J].

Ezzinbi, Khalil ;

Toure, Hamidou ;

Zabsonre, Issa .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (09) :3378-3389

[8] EXISTENCE OF SOLUTIONS FOR NEUTRAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS [J].

Fu, Xianlong ;

Gao, Yan ;

Zhang, Yu .

TAIWANESE JOURNAL OF MATHEMATICS, 2012, 16 (05) :1879-1909

[9] SERIES EXPANSIONS FOR RESOLVENTS OF VOLTERRA INTEGRODIFFERENTIAL EQUATIONS IN BANACH-SPACE [J].

GRIMMER, RC ;

KAPPEL, F .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1984, 15 (03) :595-604

[10] RESOLVENT OPERATORS FOR INTEGRAL-EQUATIONS IN A BANACH-SPACE [J].

GRIMMER, RC .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 273 (01) :333-349

← 1 2 3 4 →