Results 181 to 190 of about 3,006,945 (193)

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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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_ ...
Minggen Cui, Hong Du
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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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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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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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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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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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Nonlinear Volterra integral equations and the Schröder functional equation

Nonlinear Analysis: Theory, Methods & Applications, 2011
The author shows an interesting connection between a special class of Volterra integral equations with convolution kernels \[ u(t)=\int\limits_{0}^{t}k(t-s)g(u(s)ds, \quad g(0)=0, \quad t\geq 0, \] and the famous Schröder equation \[ F(h(x))=cF(x),\quad x\in I.
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System of nonlinear Volterra’s integral equations with polar kernel and singularities

Nonlinear Analysis: Theory, Methods & Applications, 2007
Using one special Colombeau algebra and the method of regularization of fractional derivatives with a delta sequence, the author proves the existence and the uniqueness of the solution of a system of nonlinear Volterra integral equations with polar kernel.
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Nonlinear Volterra Integral Equations

2015
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