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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Şevgin, Sebaheddin 2014. Numerical solution of a singularly perturbed Volterra integro-differential equation. Advances in Difference Equations, Vol. 2014, Issue. 1, p. 171.

    Khater, A. H. Shamardan, A. B. Callebaut, D. K. and Sakran, M. R. A. 2007. Numerical solutions of integral and integro-differential equations using Legendre polynomials. Numerical Algorithms, Vol. 46, Issue. 3, p. 195.

    Amiraliyev, G.M. and Şevgin, Sebaheddin 2006. Uniform difference method for singularly perturbed Volterra integro-differential equations. Applied Mathematics and Computation, Vol. 179, Issue. 2, p. 731.

    Jordan, G. S. 1979. Volterra Equations.

    Nohel, John A. 1979. Functional Differential Equations and Approximation of Fixed Points.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 80, Issue 3-4
  • January 1978, pp. 235-247

A nonlinear singularly perturbed Volterra integrodifferential equation of nonconvolution type

  • G. S. Jordan (a1)
  • DOI:
  • Published online: 14 November 2011

We consider the nonconvolution initial value problem

where μ is a small positive parameter, b(t, s) is a given real kernel, and F, g are given real functions. For the convolution case b(t,s) = a(t − s). Lodge, McLeod, and Nohel recently established many qualitative properties of the solution of (+); we extend their results to the general nonconvolution problem. In particular, conditions are given that ensure that the solution of (+) decreases to a limiting value α(μ) > 1 as t → ∞.

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1T. R. Kiffe On Nonlinear Volterra Equations of Nonconvolution Type. J. Differential Equations 22 (1976), 349367.

2J. J. Levin A Nonlinear Volterra Equation not of Convolution Type. J. Differential Equations 4 (1968), 176186.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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