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Linear Volterra Integral Equations
Acta Mathematicae Applicatae Sinica, English Series, 2002The 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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2011
This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Jie Shen, Tao Tang, Li-Lian Wang
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This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Jie Shen, Tao Tang, Li-Lian Wang
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2021
We extend the recently developed rough path theory to the case of more rough noise and/or more singular Volterra kernels. It was already observed that the Volterra rough path introduced there did not satisfy any geometric relation, similar to that observed in classical rough path theory.
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We extend the recently developed rough path theory to the case of more rough noise and/or more singular Volterra kernels. It was already observed that the Volterra rough path introduced there did not satisfy any geometric relation, similar to that observed in classical rough path theory.
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1999
In this chapter first we shall follow Meehan and O’Regan [213,215] and present results which guarantee the existence of nonnegative solutions of the Volterra integral equation $$y\left( t \right) = h\left( t \right) - \int_0^t {k\left( {t,s} \right)} g\left( {s,y\left( s \right)} \right)ds,t \in {\text{ }}\left[ 0 \right.
Ravi P. Agarwal +2 more
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In this chapter first we shall follow Meehan and O’Regan [213,215] and present results which guarantee the existence of nonnegative solutions of the Volterra integral equation $$y\left( t \right) = h\left( t \right) - \int_0^t {k\left( {t,s} \right)} g\left( {s,y\left( s \right)} \right)ds,t \in {\text{ }}\left[ 0 \right.
Ravi P. Agarwal +2 more
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Journal of Soviet Mathematics, 1979
One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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Singularly Perturbed Volterra Integral Equations
SIAM Journal on Applied Mathematics, 1987The authors study the singularly perturbed Volterra integral equation \[ \epsilon u(t)=\int^{t}_{0}K(t-s)F(u(s),s) ds,\quad t\geq 0, \] where \(\epsilon\) is a small parameter, with the objective of developing a methodology that yields the appropriate ''inner'' and ''outer'' integral equations, each of which is defined on the whole domain of interest ...
Angell, J. S., Olmstead, W. E.
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On a nonlinear volterra equation
Mathematical Methods in the Applied Sciences, 1986AbstractNonnegative solutions u of the nonlinear Volterra equation u = a * g(u) (g(0) = 0) in mathematical physics are considered. Under certain assumptions the nonhomogenuous equation u = a * g(u) + ƒ is studied. Some approximations of nonnegative solutions of the homogenuous equation are considered by the nonnegative solutions of the nonhomogenuous ...
W. Okrasiński Wroclaw, E. Meister
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