Results 181 to 190 of about 1,156,539 (216)

Structure of Solutions of Volterra Equations

SIAM Review, 1983
This paper presents an elementary introduction to linear Volterra integral and integro-differential equations. 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 ...
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Floquet Theory for a Volterra Equation

Journal of the London Mathematical Society, 1988
The authors discuss periodic solutions of the integrodifferential equation \[ dy(t)/dt=A(t)y(t)+\int^{t}_{0}C(t,s)y(s)ds+f(t), \] relating two different integrability properties of the resolvent to each other.
Becker, L. C., Burton, T. A., Krisztin, T.   +2 more
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On volterra equations of the first kind

Integral Equations and Operator Theory, 1980
The existence of a solution β of the equation $$\int_0^t {a(t - s)d\beta (s) = 1, t > 0} $$ is studied under fairly general assumptions on the function a. Sufficient conditions for the measure β to be absolutely continuous or satisfy some additional regularity properties are given. An extension to nonconvolution kernels is also considered.
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Volterra-Type Equations in S ′+

Mathematical Notes, 2004
Necessary and sufficient condition for the unique solvability of Volterra integro-differential equation in \(S\prime _ + \) is given.
Pilipović, Stevan, Stojanović, Mirjana
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On a Nonlinear Hyperbolic Volterra Equation

SIAM Journal on Mathematical Analysis, 1980
We study questions of existence, boundedness and asymptotic behavior of the solutions of the initial value problem \[(*)\qquad \begin{array}{*{20}c} {u_t (t,x) - \int_0^t {a (t - s)\sigma (u_x (s,x))_x = f(t,x),\quad 0 < t < \infty ,\quad x \in R.} } \\ {u(0,x) = u_0 (x),\quad x \in R.} \\ \end{array} \] Here $a:R^ + = [0,\infty ) \to R,\sigma :R \to R,
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A Volterra Equation with a Nonconvolution Kernel

SIAM Journal on Mathematical Analysis, 1977
This paper is concerned with the asymptotic behavior of solutions of the Volterra integral equation \[x(t) + \int_0^t {a(t,\tau )g(x(\tau ))d\tau = f(t)} ,\quad 0 \leqq t < \infty \] If $x(t)$ is a solution of this equation, the limiting values of $g(x(t))$ are given under various sets of hypotheses on the kernel $a(t,\tau )$ and the functions $g(t ...
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Bounded Solutions of Volterra Equations

SIAM Journal on Mathematical Analysis, 1988
The author studies the existence of bounded solutions of the equation \[ (1)\quad u'(t)=Au(t)+\int^{\infty}_{0}dB(\tau)u(t-\tau)+f(t),\quad t\in {\mathbb{R}}, \] in a Banach space X. Here A is a closed linear operator with dense domain D(A) and \(B\in BV({\mathbb{R}}_+,B(D(A),X))\).
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Volterra Equation

2022
Jocelyn Sabatier, Christophe Farges, Vincent Tartaglione   +2 more
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On Volterra’s Population Equation with Diffusion

SIAM Journal on Mathematical Analysis, 1985
Summary: In this paper Volterra's population equation with diffusion for a single, isolated species \(u\) is considered. Generalizing a result of \textit{R. K. Miller} [SIAM J. Appl. Math. 14, 446-452 (1966; Zbl 0161.31901)] it is shown that every nonnegative solution \(u\not\equiv 0\) tends, as \(t\to \infty\), to a spatially homogeneous distribution \
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On Volterra’s Population Equation

SIAM Journal on Applied Mathematics, 1966
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