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Integrability of Resolvents of Systems of Volterra Equations
SIAM Journal on Mathematical Analysis, 1981The integrability of the resolvents of systems of Volterra integral and integrodifferential equations is studied. The matrix kernels in the equations need not be integrable, and some of the conditions used are shown to be both necessary and sufficient.
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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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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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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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On the Asymptotic Behavior of Volterra Integral Equations
SIAM Journal on Mathematical Analysis, 1972Suppose $y(t) = f(t) - \int_0^t {a(t,s)y(s)ds} $ is a system of Volterra integral equations, and let $r(t,s)$ be the resolvent kernel corresponding to this system. If $f(t)$ is continuous and $\omega $-periodic, it is shown that under suitable restrictions on $r(t,s)$, the solution $y(t)$ is asymptotically $\omega $-periodic.
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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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On Volterra–Fredholm Equations with Partial Integrals
Differential Equations, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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VOLTERRA INTEGRAL EQUATIONS AND NONLINEAR SEMIGROUPS
Nonlinear Analysis: Theory, Methods & Applications, 1977Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
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