On qualitative properties in Volterra integro-differential equations

被引：3
作者：
Tunc, Cemil [1 ]
机构：
[1] Yuzuncu Yil Univ, Fac Sci, Dept Math, TR-65080 Van, Turkey
来源：
ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES | 2017年 / 1798卷
关键词：
STABILITY;
D O I：
10.1063/1.4972756
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this research, we utilize a Lyapunov function and obtain sufficient conditions for the asymptotically stability and boundedness of solutions to the Volterra integro-differential equations of the form d/dt[x(t) - integral D-t(0)(t, s)x(s)ds] = -A(t)x(t) + integral(t)(0) C(t, s)x(s)ds + e(t, x). The obtained results revise, correct and improve the results obtained in literature.
引用
收藏
页数：9
相关论文
共 18 条
[1]  
[Anonymous], 2009, CUBO
[2]  
Burton T. A., 2005, VOLTERRA INTEGRAL DI, P1
[3]   STABILITY BY DECOMPOSITIONS FOR VOLTERRA-EQUATIONS [J].
BURTON, TA ;
MAHFOUD, WE .
TOHOKU MATHEMATICAL JOURNAL, 1985, 37 (04) :489-511
[4]   STABILITY THEORY FOR VOLTERRA EQUATIONS [J].
BURTON, TA .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 32 (01) :101-118
[5]   CONSTRUCTION OF LIAPUNOV FUNCTIONALS FOR VOLTERRA-EQUATIONS [J].
BURTON, TA .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1982, 85 (01) :90-105
[6]   RATE OF DECAY OF SOLUTIONS OF VOLTERRA-EQUATIONS [J].
BURTON, TA ;
HUANG, QC ;
MAHFOUD, WE .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1985, 9 (07) :651-663
[7]  
Furumochi T., 1999, MEM FS ENG SHIMANE U, V32, P25
[8]  
Grace S. R., 2013, PAN AM MATH, V23, P35
[9]   Continuability and boundedness of multi-delay functional integro-differential equations of the second order [J].
Graef, John R. ;
Tunc, Cemil .
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2015, 109 (01) :169-173
[10]  
Hara T., 1990, FUNKC EKVACIOJ-SER I, V33, P39
12