Volterra–Stieltjes integral equations and impulsive Volterra–Stieltjes integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper, we prove existence and uniqueness of solutions of Volterra–Stieltjes integral equations using the Henstock–Kurzweil integral. Also, we prove that these equations encompass impulsive Volterra–Stieltjes integral equations and prove the ...
Edgardo Alvarez +3 more
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Existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra ...
dingshi li, Daoyi Xu
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Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation. [PDF]
PLoS ONE, 2023 A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral ...
A Z Amin +4 more
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Admissibility and Nonlinear Volterra Integral Equations [PDF]
Proceedings of the American Mathematical Society, 1970 Nonlinear perturbations of linear Volterra integral equations are studied in an abstract setting which contains and generalizes some earlier results on the same problem. The perturbed problem is first written as a variation of constants equation on a Fréchet space.
Richard K. Miller
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On the oscillation of a Volterra integral equation [PDF]
Czechoslovak Mathematical Journal, 1995 The author studies oscillation criteria for the integral equation \[ X(t)= f(t)- \int^t_0 a(t, s) g(s, X(s)) ds,\quad t\geq 0.\tag{\(*\)} \] Sufficient conditions for all solutions of equation \((*)\) to oscillate as well as growth estimates for the solutions are given.
Bhagat Singh
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A Kneser Theorem for Volterra Integral Equations [PDF]
Proceedings of the American Mathematical Society, 1973 A connectedness result is obtained for the space of solutions of any one of a class of Volterra integral equations.
Walter G. Kelley
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Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine [PDF]
Frontiers in Computational Neuroscience, 2023 In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm.
Yanfei Lu +3 more
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A Volterra integral equation of the first kind
Journal of Mathematical Analysis and Applications, 1976 In animal studies of the effect of the deposition of radioactive debris in the lung, use is made of very small spheres (about 10 ..mu..m diameter) of ZrO/sub 2/ impregnated with plutonium, an ..cap alpha..-particle emitter. A quality control problem that arises in the manufacture of these spheres is that of determining the radial density distribution ...
W. L. Hendry
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Oscillations of Volterra integral equations with delay [PDF]
Tohoku Mathematical Journal, 1993 Consider the Volterra integral equation with delays \(x(t)=f(t)-\int_ 0^ t K(t,s,x_ s)ds\), \(t\geq 0\), where \(f\in C(\mathbb{R}^ +,\mathbb{R})\), \(K(t,s,\varphi)\) is continuous in \(t\) and \(\varphi\), and maps bounded sets into bounded sets.
Karakostas, George +2 more
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On the inversion of the Volterra integral equation [PDF]
Quarterly of Applied Mathematics, 1952 B. Groß
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