Results 171 to 180 of about 1,156,539 (216)

Positive quadratures for volterra equations

Computing, 1976
The present paper deals with discretizations to linear Volterra equations which preserve the possible positivity of the Volterra operator. It is shown that the method must be implicit and e.g. that the repeated trapezoidal rule has this property. It is then shown how this property can be used in studying the asymptotic behaviour of the solutionsx
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Linear Volterra Integral Equations

Acta Mathematicae Applicatae Sinica, English Series, 2002
The authors apply the Kurzweil-Henstock integral formalism to give existence theorems for linear Volterra equations \[ x(t)+^{\ast}\int_{[a,t]}\alpha(s)x(s)\,ds=f(t),\qquad t\in[ a,b],\tag{1} \] where the functions \(x,f\)\ have values in the Banach space \(X\).
Federson, M., Bianconi, R., Barbanti, L.
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Stability of Volterra Difference Equations

Differential Equations, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kolmanovskii, V. B., Kosareva, N. P.
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Eigenvalues and Nonlinear Volterra Equations

1995
This paper is devoted to present a solution to the eigenvalue problem for non-linear Volterra operators having the form $$ Tu(x) = \int_0^x {k(x - s)g(u(s))} ds $$ .
Arias M., Castillo J., SIMOES, Marilda
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A volterra-type integral equation

Ukrainian Mathematical Journal, 1989
See the review in Zbl 0653.45005.
Ashirov, S., Mamedov, Ya. D.
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A Perturbation of an Abstract Volterra Equation

SIAM Journal on Mathematical Analysis, 1980
This paper discusses the existence of solutions to equations of the form $u(t,x) + \smallint _0^t a(t - s)[Au(s,x) + g(u(s,x))]ds = f(t,x)$ where A is a differential operator on $L^2 (\Omega ),\Omega $ a bounded open subset of $R^n $, and g is a discontinuous real-valued function which is not necessarily monotone increasing.
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A Volterra Equation in Hilbert Space

SIAM Journal on Mathematical Analysis, 1974
This paper concerns the asymptotic behavior of the solution of a Volterra equation in Hilbert space. The proof uses spectral decomposition and a result of independent interest on the global dependence on a parameter of the solution of a scalar integro-differential equation.
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On a random Volterra integral equation

Mathematical Systems Theory, 1973
Tsokos [12] showed the existence of a unique random solution of the random Volterra integral equation (*)x(t; ω) = h(t; ω) + ∫ k(t, τ; ω)f(τ, x(τ; ω)) dτ, whereω ∈ Ω, the supporting set of a probability measure space (Ω,A, P)
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On a semilinear volterra integrodifferential equation

Israel Journal of Mathematics, 1980
The Volterra integrodifferential equation $$\begin{array}{*{20}c} {u_t (t,x) + \smallint '_0 a(t - s)( - \Delta u(s,x) + f(x,u(s,x)))ds = h(t,x),,} \\ {t > 0,x \in \Omega \subset R^N ,} \\ \end{array} $$ together with boundary and initial conditions is considered.
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An Equation of Volterra

1971
Consider the system $${\rm{A\:x}}\left( {\rm{t}} \right) + {\rm{Bx}}\left( {\rm{t}} \right) = \int_0^{\rm{r}} {{\rm{F}}\left( \theta \right){\rm{x}}\left( {{\rm{t}} - \theta } \right)} {\rm{d}}\theta $$ (15.1) where A,B,F are symmetric n × n matrices and F is continuously differentiable. Let $${\rm{M}} = {\rm{B}} - \int_0^{\rm{r}} {{\rm{F}
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