Results 211 to 220 of about 26,735 (243)
Some of the next articles are maybe not open access.
A volterra-type integral equation
Ukrainian Mathematical Journal, 1989See the review in Zbl 0653.45005.
S. Ashirov, Ya. D. Mamedov
openaire +3 more sources
2011
This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Li-Lian Wang, Tao Tang, Jie Shen
openaire +4 more sources
This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Li-Lian Wang, Tao Tang, Jie Shen
openaire +4 more sources
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 $$y\left( t \right) = h\left( t \right) - \int_0^t {k\left( {t,s} \right)} g\left( {s,y\left( s \right)} \right)ds,t \in {\text{ }}\left[ 0 \right.
Donal O'Regan +2 more
openaire +2 more sources
In this chapter first we shall follow Meehan and O’Regan [213,215] and present results which guarantee the existence of nonnegative solutions of the Volterra integral equation $$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.
Donal O'Regan +2 more
openaire +2 more sources
Volterra Integral Equations [PDF]
, 1995 As shown by equations (1.1.1–2), there is a close relationship between ordinary differential equations and Volterra integral equations. First, we discuss the unique solvability. Afterwards, in §2.1.2, we discuss the regularity of the solution.
openaire +1 more source
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)
openaire +2 more sources
On Volterra-Fredholm integral equations
Periodica Mathematica Hungarica, 1993The Ważewski method associated with the convergence of successive approximations is used in order to obtain existence and uniqueness results for the functional-integral equation of Volterra-Fredholm type of the form \[ \begin{multlined} x(t)=F \Biggl( t,x(t), \int_ 0^ t f_ 1(t,s,x(s))ds,\dots, \int_ 0^ t f_ n(t,s,x(s))ds,\\ \int_ 0^ T g_ 1(t,s,x(s))ds,\
openaire +2 more sources
On a weakly singular Volterra integral equation
CALCOLO, 1981The need for providing reliable numerical methods for the solution of weakly singular Volterra integral equations of first kind stems from the fact that they are connected to important problems in the theory and applications of stochastic processes. In the first section the above problems and some peculiarities of such equations are briefly sketched ...
E. M. De Griffi, L. F. Favella
openaire +4 more sources
2012
In this chapter, our attention is devoted to the Volterra integral equation of the second kindwhich assumes the form $$\phi (x) = f(x) + \lambda \,{\int \nolimits }_{a}^{x}\,K(x,t)\,\phi (t)\,\mathrm{d}t.$$ (4.1) Volterra integral equations differ from Fredholm integral equations in that the upper limit of integration is the variable x ...
openaire +2 more sources
In this chapter, our attention is devoted to the Volterra integral equation of the second kindwhich assumes the form $$\phi (x) = f(x) + \lambda \,{\int \nolimits }_{a}^{x}\,K(x,t)\,\phi (t)\,\mathrm{d}t.$$ (4.1) Volterra integral equations differ from Fredholm integral equations in that the upper limit of integration is the variable x ...
openaire +2 more sources
1970
In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
openaire +2 more sources
In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
openaire +2 more sources
2016
In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
openaire +2 more sources
In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
openaire +2 more sources