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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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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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Volterra Integral Dynamic Equations
2020In this chapter, we apply the concept of resolvent that we developed in Sect. 1.4.1 for vector Volterra integral dynamic equations and show the boundedness of solutions. The resolvent is an abstract term which makes it difficult, if not impossible, to make efficient use of it. However, by the help of Lyapunov functionals and variation of parameters, we
Murat Adıvar, Youssef N. Raffoul
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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 ...
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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 ...
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Singularly Perturbed Volterra Integral Equations II
SIAM Journal on Applied Mathematics, 1987The authors extend the formal methodology for the asymptotic analysis of singularly perturbed Volterra integral equations developed by themselves [ibid. 47, 1-14 (1987; Zbl 0616.45009)] to several problems of the form \[ \epsilon (a(\epsilon)u'(t)+b(\epsilon)u(t))=\int^{t}_{0}k(t,s;\epsilon)f[u(s),s ;\epsilon]\quad ds+f(t;\epsilon),\quad t\geq 0 ...
Angell, J. S., Olmstead, W. E.
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2017
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels ...
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This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels ...
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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.
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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.
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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.
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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.
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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]}.
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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]}.
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$L^2 $ Solutions of Volterra Integral Equations
SIAM Journal on Mathematical Analysis, 1979The existence of a unique $L^2 [0,T;H]$ solution of the equation $u(t) + \int_0^t {a(t - s)g(u(s))ds \ni f(t)} $ is shown for any $L^2 [0,T;H]$ function $f(t)$ where g is any maximal monotone operator satisfying a linear growth condition.
Kiffe, T., Stecher, M.
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