ABSTRACT NON-LINEAR VOLTERRA EQUATION

被引：11
作者：
GRIPENBERG, G [1 ]
机构：
[1] UNIV WISCONSIN,DEPT MATH,MADISON,WI 53706
来源：
ISRAEL JOURNAL OF MATHEMATICS | 1979年 / 34卷 / 03期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/BF02760883
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The existence, uniqueness, regularity and dependence upon data of solutions of the abstract Volterra equation u(t)+∫ 0 t a(t-s)A(u(s))ds∈f(t), t≧0 are studied in a real Banach space. The nonlinear operator A is assumed to be m-accretive and the assumptions on the kernel a do not exclude the possibility that lim t→0+ a(t)=+∞. © 1979 Hebrew University.
引用
收藏
页码：198 / 212
页数：15
相关论文
共 50 条
[31]   On an analogy between the non-linear pendulum equation and the Lotka-Volterra system [J].
Teodoresu, P.P. ;
Toma, Ileana .
Revue Roumaine des Sciences Techniques, Serie de Mecanique Appliquee, 1994, 39 (05)
[32]   USE OF VOLTERRA SERIES TO FIND REGION OF STABILITY OF A NON-LINEAR DIFFERENTIAL EQUATION [J].
BARRETT, JF .
INTERNATIONAL JOURNAL OF CONTROL, 1965, 1 (03) :209-&
[33]   AN ABSTRACT SEMI-LINEAR HYPERBOLIC VOLTERRA INTEGRODIFFERENTIAL EQUATION [J].
HEARD, ML .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 80 (01) :175-202
[34]   NON-LINEAR ABSTRACT HYPERBOLIC EQUATIONS [J].
YAKUBOV, SY .
DOKLADY AKADEMII NAUK SSSR, 1967, 176 (01) :46-&
[35]   PERTURBED NON-LINEAR ABSTRACT EQUATIONS [J].
VEJVODA, O ;
STRASKRABA, I .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1981, 5 (03) :265-276
[36]   CONDITIONS FOR ABSTRACT NON-LINEAR REGULATION [J].
SONTAG, ED .
INFORMATION AND CONTROL, 1981, 51 (02) :105-127
[37]   Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay [J].
Zhang, Li ;
Huang, Jin ;
Li, Hu ;
Wang, Yifei .
MATHEMATICS, 2021, 9 (16)
[38]   A Volterra series approach to the frequency domain analysis of non-linear viscous Burgers' equation [J].
Guo, L. Z. ;
Guo, Y. Z. ;
Billings, S. A. ;
Coca, D. ;
Lang, Z. Q. .
NONLINEAR DYNAMICS, 2012, 70 (03) :1753-1765
[39]   EXISTENCE RESULT FOR A NON-LINEAR VOLTERRA INTEGRAL-EQUATION IN A HILBERT-SPACE [J].
GRIPENBERG, G .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1978, 9 (05) :793-805
[40]   A Volterra series approach to the frequency domain analysis of non-linear viscous Burgers’ equation [J].
L. Z. Guo ;
Y. Z. Guo ;
S. A. Billings ;
D. Coca ;
Z. Q. Lang .
Nonlinear Dynamics, 2012, 70 :1753-1765
12345