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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Qualitative Properties of Nonlinear Volterra Integral Equations
TL;DR: In this article, the contraction mapping principle and Liapunov method are used to study qualitative properties of nonlinear Volterra equations of the form x = a(t) Z t 0 C(t,s)g(s,x(s)) ds,t � 0.
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Structure of Solutions of Volterra Equations
TL;DR: In this paper, an elementary introduction to linear Volterra integral and integro-differential equations is presented, and it is demonstrated that the theory of existence, uniqueness, dimensionality of the solution space, and the variation of parameters formula are virtually indistinguishable from the corresponding elementary theory of ordinary differential equations.
Analysis of Gain Scheduled Control for Linear Parameter-Varying Plants'
TL;DR: In this paper, the authors present an analysis for one type of gain scheduled system, namely, a linear parameter-varying plant scheduling on its exogenous parameters, and conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain scheduled design.
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Qualitative analysis of nonlinear Volterra integral equations on time scales using resolvent and Lyapunov functionals
Murat Adıvar,Youssef N. Raffoul +1 more
TL;DR: The existence of bounded solutions with various Lp properties are studied under suitable conditions on the functions involved in the above Volterra integral equation.
References
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Fourier Transforms in the Complex Domain
TL;DR: In this article, a generalized harmonic analysis in the complex domain of random functions has been proposed, based on Szasz's theorem and a class of singular integral equations of the exponential type.
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Problèmes globaux dans le théorie des équations intégrales de Volterra
TL;DR: In this paper, theoremes de point fixe and d'autres moyens de l' Analyse fonctionnelle are used to compute the solutions of equations integrales non-lineaires.
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On the linearization of Volterra integral equations.
TL;DR: Volterra integral equations linearization, discussing integral kernels, integrodifferential equations and reactor dynamics was discussed in this paper, where integral kernels and integro-linear equations were discussed.
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Indirect abelian theorems and a linear Volterra equation
TL;DR: In this article, the authors define u(t) as the solution of (1.1) with k = O, xo = 1, and w(t), q = ft u(Q) dJ.