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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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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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A volterra-type integral equation
Ukrainian Mathematical Journal, 1989See the review in Zbl 0653.45005.
Ashirov, S., Mamedov, Ya. D.
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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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On a random Volterra integral equation
Mathematical Systems Theory, 1973Tsokos [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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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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VOLTERRA INTEGRAL EQUATIONS [PDF]
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006 One of the current active areas of research in mathematics is the study of Volterra integral equations. Many applied problems lead to obtaining solutions of Volterra type integral equations.
Grigoryan, Anzhela
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On integral equations of Urysohn–Volterra type
Applied Mathematics and Computation, 2003The existence of solutions to Urysohn-Volterra integral equations in a locally convex topological Hausdorff space is established using the Schauder-Tychonoff theorem.
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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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