Volterra integral equations

One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.

[1]  Bounded solutions of Stieltjes integral equations , 1971 .

[2]  Pierre Verbaeten,et al.  Numerical solution of the abel integral equation , 1973 .

[3]  Peter Linz,et al.  A method for solving nonlinear Volterra integral equations of the second kind , 1969 .

[4]  J. Kaplan.  On the Asymptotic Behavior of Volterra Integral Equations , 1972 .

[5]  Dichotomies for differential and integral equations , 1973 .

[6]  Positive definite functions and Volterra integral equations , 1974 .

[7]  G. Porath.  Störungsrechnung für lineare VOLTERRASche Integralgleichungen , 1968 .

[8]  A stability theorem for nonlinear mixed integral equations , 1969 .

[9]  Numerical solution of the convolution integral equation , 1969 .

[10]  The numerical solution of volterra intergral equations with singular kernels , 1974 .

[11]  B. Noble.  Instability when solving Volterra integral equations of the second kind by multistep methods , 1969 .

[12]  C. Corduneanu.  Problèmes globaux dans le théorie des équations intégrales de Volterra , 1965 .

[13]  A Volterra integral equation in the stability of some linear hereditary phenomena , 1968 .

[14]  V. Lakshmikantham,et al.  Some point-wise estimates for solutions of a class of nonlinear functional-integral inequalities , 1972 .

[15]  On spline function approximations to the solution of volterra integral equations of the first kind , 1974 .

[16]  B. G. Pachpatte,et al.  A note on Gronwall-Bellman inequality , 1973 .

[17]  F. Hoppensteadt,et al.  Asymptotic Behavior of Solutions to a Population Equation , 1975 .

[18]  Admissibility and nonlinear Volterra integral equations , 1970 .

[19]  On a system of integral inequalities , 1967 .

[20]  K. Deimling.  A Carathéodory theory for systems of integral equations , 1970 .

[21]  Constantin Corduneanu,et al.  Integral Equations and Stability of Feedback Systems , 1973 .

[22]  A. N. Godunov,et al.  Peano's theorem in Banach spaces , 1975 .

[23]  C. S. Hönig.  Volterra-Stieltjes integral equations with linear constraints and discontinuous solutions , 1975 .

[24]  F. Hoog,et al.  Implicit Runge-Kutta methods for second kind Volterra integral equations , 1974 .

[25]  J. Reneke.  A product integral solution of a Stieltjes-Volterra integral equation. , 1970 .

[26]  B. Helton.  The solution of a nonlinear Gronwall inequality , 1973 .

[27]  V. Vinokurov,et al.  Optimal Control of Processes Described by Integral Equations, III , 1969 .

[28]  Robert S. Anderssen,et al.  A product integration method for a class of singular first kind Volterra equations , 1971 .

[29]  V. Mizel,et al.  On fading memory spaces and hereditary integral equations , 1974 .

[30]  Sadao Sugitani,et al.  On nonexistence of global solutions for some nonlinear integral equations , 1975 .

[31]  W. R. Mann,et al.  On a certain nonlinear integral equation of the Volterra type. , 1951 .

[32]  Chi-Tsong Chen.  Bounded input bounded-output stability of linear time-varying feedback systems , 1968 .

[33]  M. Suryanarayana.  On multidimensional integral equations of Volterra type. , 1972 .

[34]  R. K. Miller,et al.  On Volterra integral equations with nonnegative integrable resolvents , 1968 .

[35]  A. Friedman.  Periodic behavior of solutions of Volterra integral equations , 1965 .

[36]  S. McKee,et al.  Multistep Methods for Solving Linear Volterra Integral Equations of the First Kind , 1975 .

[37]  G. Sell,et al.  Existence, uniqueness and continuity of solutions of integral equations , 1968 .

[38]  Stability of perturbed Volterra integral equations , 1975 .

[39]  J. J. Levin.  The qualitative behavior of a nonlinear Volterra equation , 1965 .

[40]  J. C. Helton,et al.  Solution of integral equations by product integration , 1975 .

[41]  G. Campbell,et al.  The numerical solution of nonlinear Volterra integral equations , 1970 .

[42]  Z. Artstein.  Continuous Dependence of Solutions of Volterra Integral Equations. , 1975 .

[43]  A gradient method for systems described by integral equations , 1973 .

[44]  B. G. Pachpatte,et al.  On some generalizations of Bellman's Lemma , 1975 .

[45]  K. Stewartson.  On an integral equation , 1968 .

[46]  A. G Petsoulas,et al.  The approximate solution of Volterra integral equations , 1975 .

[47]  The Solution of Volterra Integral Equations of the First Kind by Piecewise Polynomials , 1973 .

[48]  W. Walter.  Differential and Integral Inequalities , 1970 .

[49]  I. Sandberg,et al.  On Generalizations and Extensions of the Popov Criterion , 1966 .

[50]  Aaron Strauss.  On a perturbed Volterra integral equation , 1970 .

[51]  Richard Weiss,et al.  High Order Methods for Volterra Integral Equations of the First Kind , 1973 .

[52]  Alan Feldstein,et al.  Smoothness of solutions of Volterra integral equations with weakly singular kernels , 1971 .

[53]  E. Rakotch.  Numerical solution of Volterra integral equations , 1972 .

[54]  V. Barbu.  Nonlinear Volterra Equations in a Hilbert Space , 1975 .

[55]  H. Maeda.  Stability Considerations for a Volterra Integral Equation with Discontinuous Nonlinearity , 1973 .

[56]  Peter Linz,et al.  Numerical methods for Volterra integral equations of the first kind , 1969, Comput. J..

[57]  Aaron Strauss.  A discussion of the linearization of volterra integral equations , 1970 .

[58]  Richard Weiss,et al.  Product Integration for the Generalized Abel Equation , 1972 .

[59]  W. Kelley.  A Kneser theorem for Volterra integral equations , 1973 .

[60]  Richard K Miller,et al.  Nonlinear Volterra Integral Equations , 1970 .

[61]  S. Deo,et al.  Pointwise estimates of solutions of some volterra integral equations , 1974 .

[62]  A Volterra Equation with Parameter , 1973 .

[63]  R. P. Srivastav.  On Certain Integral Equations of Convolution Type with Bessel-Function Kernels , 1966, Proceedings of the Edinburgh Mathematical Society.

[64]  D. Hinton.  A Stieltjes–Volterra Integral Equation Theory , 1966, Canadian Journal of Mathematics.

[65]  L. Garey,et al.  Solving Nonlinear Second Kind Volterra Equations by Modified Increment Methods , 1975 .

[66]  Convergence theorems for solutions of a certain Volterra integral equation , 1970 .

[67]  The fredholm and volterra problems for stieltjies integral equations , 1975 .

[68]  On the properties of nonlinear integral equations that arise in the theory of dynamical systems , 1964 .

[69]  H. Brunner.  On the approximate solution of the abel integral equation with discontinuous solution , 1975 .

[70]  J. T. Day,et al.  A Starting Method for Solving Nonlinear Volterra Integral Equations , 1967 .

[71]  A. Friedman.  Monotonicity of solutions of Volterra integral equations in Banach space , 1969 .

[72]  On the numerical stability of spline function approximations to solutions of Volterra integral equations of the second kind , 1974 .

[73]  G. Butler,et al.  A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations , 1971 .

[74]  J. Cushing,et al.  A representation formula for linear Volterra integral equations , 1973 .

[75]  Existence and stability behaviour of a non-linear perturbed stochastic system , 1974 .

[76]  Stephen Wainger,et al.  Variants of the Wiener-Levy Theorem, with Applications to Stability Problems for Some Volterra Integral Equations , 1975 .

[77]  Avner Friedman,et al.  Volterra integral equations in Banach space , 1967 .

[78]  J. J. Levin.  A bound on the solutions of a Volterra equation , 1973 .

[79]  T. R. Prabhakar.  Some Integral Equations with Rummer's Functions in the Kernels , 1971, Canadian Mathematical Bulletin.

[80]  M. L. Klasi,et al.  The Gronwall inequality for weighted integrals , 1971 .

[81]  On the numerical solution of linear volterra integral equations , 1967 .

[82]  R. K. Miller.  Asymptotically Almost Periodic Solutions of a Nonlinear Volterra System , 1971 .

[83]  K. Hannsgen.  A Linear Volterra Equation in Hilbert Space , 1974 .

[84]  A. F. Izé.  On an asymptotic property of a Volterra integral equation , 1971 .

[85]  A. Ostrowski.  On an integral inequality , 1970 .

[86]  P. Sigmund.  A note on integral equations of the kinchin-pease type , 1969 .

[87]  G. Sell.  A tauberian condition and skew product flows with applications to integral equations , 1973 .

[88]  G. Campbell,et al.  A block by block method for the numerical solution of Volterra integral equations , 1971 .

[89]  Limits of solutions of Volterra integral equations , 1975 .

[90]  Asymptotic relationships between systems of volterra equations , 1971 .

[91]  On a nonlinear Volterra equation , 1972 .

[92]  Richard Weiss,et al.  High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels , 1974 .

[93]  E. M. Podgaetskii,et al.  A successive approximation method for solving a non-linear Volterra integral equation of the second kind , 1970 .

[94]  S. Londen.  On the solutions of a nonlinear Volterra equation , 1972 .

[95]  J. Nohel,et al.  Perturbations of Volterra integral equations , 1969 .

[96]  A Regularization Method for the Identification of Environmental Systems , 1975 .

[98]  Gronwall’s inequality in $n$ independent variables , 1973 .

[99]  Ken Iguchi.  A starting method for solving nonlinear Volterra integral equations of the second kind , 1972, CACM.

[100]  A variation-of-parameters inequality , 1970 .

[101]  P. Bushell,et al.  On a class of Volterra and Fredholm non-linear integral equations , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[102]  Carl W. Bitzer.  Stieltjes-Volterra integral equations , 1970 .

[103]  Richard Weiss,et al.  On the solution of volterra integral equations of the first kind , 1973 .

[104]  I. G. Petrovskiĭ.  Lectures on the theory of integral equations , 1957 .

[105]  Tokui Satō.  Sur l'équation intégrale non linéaire de Volterra , 1953 .

[106]  M. E. A. El Tom.  Spline Function Approximations to the Solution of Singular Volterra Integral Equations of the Second Kind , 1974 .

[107]  D. Willett,et al.  A linear generalization of Gronwall’s inequality , 1965 .

[108]  On linear Volterra integral equations of convolution type , 1972 .

[109]  J. Mautz,et al.  THE NUMERICAL SOLUTION OF A VOLTERRA INTEGRAL EQUATION. , 1969 .

[110]  A Volterra equation with a very singular kernel , 1966 .

[111]  K. Hannsgen.  A Volterra Equation in Hilbert Space , 1974 .

[112]  J. Nohel.  Perturbations of volterra equations and admissibility , 1971 .

[113]  S. Londen.  The qualitative behavior of the solutions of a nonlinear Volterra equation. , 1971 .

[114]  Carl W. Bitzer.  Convolution, fixed point, and approximation in Stieltjes-Volterra integral equations , 1972, Journal of the Australian Mathematical Society.

[115]  L. Delves,et al.  Numerical solution of integral equations , 1975 .

[116]  R. MacCamy.  Nonlinear Volterra equations on a Hilbert space , 1974 .

[117]  L. Bittner.  Die elementaren Differential- und Integralungleichungen mit einem allgemeinen Ungleichungsbegriff† , 1968 .

[118]  J. Chamayou.  Volterra's functional integral equations of the statistical theory of damage , 1973 .

[119]  Rolf Jeltsch,et al.  Stability of quadrature rule methods for first kind volterra integral equations , 1974 .

[120]  P. Hartman.  On Differential Equations, Volterra Equations and the Function J 2 μ + Y 2 μ , 1973 .

[121]  On the asymptotic solution of a nonlinear Volterra integral equation , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[122]  A. Mcbride.  Solution of hypergeometric integral equations involving generalised functions , 1975, Proceedings of the Edinburgh Mathematical Society.

[123]  R. Hager,et al.  The nonexistence of maximum solutions of Volterra integral equations. , 1970 .

[125]  On the asymptotic behavior in the theory of Volterra integro-functional equations , 1974 .

[126]  On the set of solutions of a system of Volterra integral equations , 1970 .

[127]  Asymptotic behaviour of a class of nonlinear Volterra integral equations , 1971 .

[128]  Dennis G. Weis.  Asymptotic behavior of some nonlinear Volterra integral equations , 1975 .

[129]  S. Nakagiri,et al.  Kneser's Property of Solution Families of Non.linear Volterra Integral Equations , 1974 .

[130]  Robert H. Martin.  Bounds for solutions to a class of nonlinear integral equations , 1971 .

[131]  Arun N. Netravali.  Spline approximation to the solution of the Volterra integral equation of the second kind , 1973 .

[132]  J. Sackman,et al.  On asymptotic stability of nonlinear hereditary phenomena , 1966 .

[133]  P. Beesack.  Comparison theorems and integral inequalities for Volterra integral equations , 1969 .

[134]  George R. Sell,et al.  Volterra integral equations and topological dynamics , 1970 .

[135]  Block methods for nonlinear Volterra integral equations , 1975 .

[136]  J. Nohel.  Asymptotic equivalence of Volterra equations , 1973 .

[137]  R. K. Miller.  Almost periodic behavior of solutions of a nonlinear Volterra system , 1971 .

[138]  A. F. Izé,et al.  Asymptotic behavior and nonoscillation of Volterra integral equations and functional differential equations , 1975 .

[139]  Successive approximations in ordered vector spaces and global solutions of nonlinear Volterra integral equations , 1972 .

[140]  Admissibility and the integral equations of asymptotic theory , 1973 .

[141]  Uniform Boundedness in a Class of Volterra Equations , 1975 .

[142]  C. S. Hönig.  Volterra Stieltjes-integral Equations: Functional Analytic Methods, Linear Constraints , 1975 .

[143]  G. Sell,et al.  A note on Volterra integral equations and topological dynamics. , 1968 .

[144]  J. Cushing,et al.  Some stability theorems for systems of volterra integral equations , 1975 .

[145]  N. McClamroch.  A general adjoint relation for functional differential and Volterra integral equations with application to control , 1971 .

[146]  R. K. Miller.  Asymptotic behavior of solutions of nonlinear Volterra equations , 1966 .

[147]  W. W Schmaedeke.  Approximate solutions for Volterra integral equations of the first kind , 1968 .

[148]  B. G Pachpatte,et al.  On some integral inequalities similar to Bellman-Bihari inequalities , 1975 .

[149]  The Numerical Solution of Singular Volterra Integral Equations , 1968 .

[150]  An error estimate for Volterra integral equations , 1971 .

[151]  S. Deo,et al.  Some generalizations of Bellman-Bihari integral inequalities , 1973 .

[152]  Peter Linz.  Product integration methods for Volterra integral equations of the first kind , 1971 .

[153]  K. Atkinson.  The Numerical Solution of an Abel Integral Equation by a Product Trapezoidal Method , 1974 .

[154]  Michael A. Wolfe.  The numerical solution of non-singular integral and integro-differential equations by iteration with Chebyshev series , 1969, Comput. J..