Perturbation theory for Volterra integrodifferential systems
S.I Grossman,R.K Miller +1 more
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This article is published in Journal of Differential Equations.The article was published on 1970-11-01 and is currently open access. It has received 108 citations till now. The article focuses on the topics: Volterra integral equation & Poincaré–Lindstedt method.read more
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Resolvent operators for integral equations in a Banach space
TL;DR: In this paper, conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a Banach space, which is similar to an evolution operator for nonautonomous differential equations.
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Analytic resolvent operators for integral equations in Banach space
Ronald Grimmer,A. J. Pritchard +1 more
TL;DR: On etudie l'equation integrodifferentielle x˙(t)=A 0 x(t)+∫ 0 t B(t-s)x(s)ds+f(t), t≥ 0, x(0)=x 0 ED(A)⊂X and l'Equation integrale x(T)=∫ t a(t − s)x (s)d+f (t) dans un espace de Banach X as discussed by the authors.
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Asymptotic stability properties of linear Volterra integrodifferential equations.
TL;DR: In this article, Liapunov stability properties of solution to a certain system of Volterra integrodifferential equations are studied, and sufficient conditions for uniform stability and uniform asymptotic stability are derived in the form of a theorem.
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Nonlinear Volterra integrodifferential systems with L1-kernels☆
S.I Grossman,R.K Miller +1 more
TL;DR: In this paper, the authors studied the problem of initial v&e problems with initial values of T > 0 and showed that these problems almost always occur in applications with T = 0.
References
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Some perturbation problems in the theory of integral equations
TL;DR: Investigation of problems related to perturbed integral equations, where many physical systems are governed by such equations, and various results are derived by special choices of the operatorsA andf and of the spacesB andD.
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Theoretical and Experimental Criteria for Nonlinear Reactor Stability
TL;DR: In this article, the authors derived nonlinear asymptotic stability criteria for point-reactor systems with delayed neutron precursors and line-line line-reconstruction.
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Un analogue du principe du point fixe de Banach
TL;DR: In this article, deux theoremes concernant l'existence d'un point fixe d'une application continue, which peuvent etre utilises dans l'etude de lure asymptotique d'a solution d'one equation differentielle ou integrale.