Remarks on a nonlinear Volterra equation
W. Mydlarczyk (1991)
Annales Polonici Mathematici
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W. Mydlarczyk (1991)
Annales Polonici Mathematici
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Karmakar, Sudhangshu B. (1980)
International Journal of Mathematics and Mathematical Sciences
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G. Karakostas (1987)
Colloquium Mathematicae
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Youssef Raffoul, Habib Rai (2016)
Nonautonomous Dynamical Systems
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In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]
Jesús M. Fernández Castillo, W. Okrasinski (1991)
Extracta Mathematicae
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In mathematical models of some physical phenomena a new class of nonlinear Volterra equations appears ([5],[6]). The equations belonging to this class have u = 0 as a solution (trivial solution), but with respect to their physical meaning, nonnegative nontrivial solutions are of prime importance.
Imen Cherif, Farhat Fnaiech (2015)
International Journal of Applied Mathematics and Computer Science
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This paper is devoted to the blind identification problem of a special class of nonlinear systems, namely, Volterra models, using a real-coded genetic algorithm (RCGA). The model input is assumed to be a stationary Gaussian sequence or an independent identically distributed (i.i.d.) process. The order of the Volterra series is assumed to be known. The fitness function is defined as the difference between the calculated cumulant values and analytical equations in which the kernels and...
W. Okrasinski (1993)
Extracta Mathematicae
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Volker Reitmann (2011)
Mathematica Bohemica
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Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation. ...
Pham Huu Anh Ngoc, Le Trung Hieu (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.