Results 171 to 180 of about 3,846,782 (204)

An abstract doubly nonlinear Volterra integral equation

Funkcialaj Ekvacioj, 1993
The existence of solutions in a real Hilbert space \(\mathcal H\) of the Volterra equation \[ u(t) + \int^ t_ 0 a(t - s) A(s) \biggl( B \bigl( u(s) \bigr) \biggr) ds \ni f(t), \quad 0 \leq t \leq T \] is studied. Here \(a : \langle 0, T \rangle \to\mathbb{R}\) is a given kernel, \(A(t)\) \((t \in \langle 0, T \rangle)\) and \(B\) denote maximal ...
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Representation of Exact Solution for the Nonlinear Volterra–Fredholm Integral Equations

Applied Mathematics and Computation, 2006
This paper is concerned with the existence of the exact solution of the following nonlinear Volterra-Fredholm integral equation \[ u(x)=f(x)+Gu(x), \] where \[ Gu(x)=\lambda_{1}\int_{a}^{x}K_{1}(x,\xi)N_{1}(u(\xi))\,d\xi +\lambda_{2}\int_{a}^{b}K_{2}(x,\xi)N_{2}(u(\xi))\,d\xi, \] \(u(x)\) is the unknown function, \(u(x), \;f(x)\in W^{1}_{2}[a,b], \;N_ ...
Hong Du, Minggen Cui
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On some parameter methods for nonlinear Volterra integral equation

Applied Mathematics and Computation, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a class of nonlinear Volterra-Fredholm q-integral equations

Fractional Calculus and Applied Analysis, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear stability of direct quadrature methods for Volterra integral equations

Mathematics and Computers in Simulation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MESSINA, ELEONORA, A. Vecchio
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ON OPTIMAL CONTROL FOR NONLINEAR VOLTERRA-STIELTJES INTEGRAL EQUATIONS

IFAC Proceedings Volumes, 1983
Abstract Some results concerning the optimal control for measure differ-ential equations are generalized to the case of Volterra equations. Because of a suitable non-anticipative version of the underlying system equation, already the usual Lipschitz condition guarantees the existence of a unique solution.
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An efficient algorithm for solving nonlinear Volterra–Fredholm integral equations

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhong Chen 0008, Wei Jiang 0012
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Stability Considerations for a Volterra Integral Equation with Discontinuous Nonlinearity

SIAM Journal on Control, 1973
The asymptotic behavior of the solutions of a Volterra integral equation with discontinuous nonlinearity is investigated. The global existence of solutions is proved and some sufficient conditions for local and/or global stability are obtained by means of the Popov-type method.
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Asymptotic Solutions of Some Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1981
The asymptotic behavior of solutions of three nonlinear Volterra integral equations of the form $u(t) + \int_0^t {A(t - s)g(u(s))ds = 0} $ is studied. These equations arise from certain diffusion problems, in dimensions 1, 2 or 3, with nonlinear boundary conditions.
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On a Nonlinear Volterra-Fredholm Integral Equation

Sarajevo Journal of Mathematics
In this paper we study the existence, uniqueness and other properties of solutions of a certain nonlinear Volterra-Fredholm integral equation. The well known Banach fixed point theorem and the new integral inequality with explicit estimate are used to establish the results.   2000 Mathematics Subject Classification.
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