On a Class of Impulsive Functional-Differential Equations with Nonatomic Difference Operator

被引：4

作者：

Vlasenko, L. A. ^{[1
]}

Rutkas, A. G. ^{[1
]}

机构：

[1] Kharkov Natl Univ, Kharkov, Ukraine

来源：

MATHEMATICAL NOTES | 2014年 / 95卷 / 1-2期

关键词：

impulsive functional-differential equation; nonatomic difference operator; equation of Sobolev type; equation not of Kovalevskaya type; Sobolev space; operator pencil; Banach space; STABILITY;

D O I：

10.1134/S0001434614010040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish conditions for the existence and uniqueness of the solutions of nonlinear functional-differential equations with impulsive action in a Banach space. The equation under consideration is not solved for the derivative. It is assumed that the characteristic operator pencil corresponding to the linear part of the equation satisfies a constraint of parabolic type in the right half-plane. Applications to partial functional-differential equations not of Kovalevskaya type are considered.

引用

页码：32 / 42

页数：11

共 50 条

[1] On a class of impulsive functional-differential equations with nonatomic difference operator
L. A. Vlasenko
A. G. Rutkas
Mathematical Notes, 2014, 95 : 32 - 42
[2] THE EVOLUTION OPERATOR APPROACH TO FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH DELAY
RUESS, WM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (03) : 783 - 791
[3] Well-posed solvability of functional-differential equations with unbounded operator coefficients
Akylzhanov, R. Kh.
Vlasov, V. V.
DIFFERENTIAL EQUATIONS, 2014, 50 (09) : 1161 - 1172
[4] Stability of impulsive functional differential equations
Zhang, Yu
Sun, Jitao
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (12) : 3665 - 3678
[5] Attracting and invariant sets for a class of impulsive functional differential equations
Xu, Daoyi
Yang, Zhichun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) : 1036 - 1044
[6] ASYMPTOTIC STABILITY IN FUNCTIONAL-DIFFERENTIAL EQUATIONS
KOBAYASHI, K
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (04) : 359 - 364
[7] STABILITY THEOREMS FOR FUNCTIONAL-DIFFERENTIAL EQUATIONS
KOBAYASHI, K
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (10) : 1183 - 1192
[8] On the spectral stability of functional-differential equations
Rossovskii, L. E.
MATHEMATICAL NOTES, 2011, 90 (5-6) : 867 - 881
[9] On the spectral stability of functional-differential equations
L. E. Rossovskii
Mathematical Notes, 2011, 90 : 867 - 881
[10] METHODS FOR COMPARISON IN FUNCTIONAL-DIFFERENTIAL EQUATIONS
FERREIRA, RR
MATEMATICA APLICADA E COMPUTACIONAL, 1993, 12 (01): : 1 - 6

← 1 2 3 4 5 →