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Singular Initial Value Problem for a System of Integro‐Differential Equations

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  • Zdeněk Šmarda
  • Yasir Khan

Abstract

Analytical properties like existence, uniqueness, and asymptotic behavior of solutions are studied for the following singular initial value problem: gi(t)yi′(t)=aiyi(t)(1+fi(t,y(t),∫0+tKi(t,s,y(t),y(s))ds)), yi(0+) = 0, t ∈ (0, t0], where y = (y1, …, yn), ai > 0, i = 1, …, n are constants and t0 > 0. An approach which combines topological method of T. Ważewski and Schauder′s fixed point theorem is used. Particular attention is paid to construction of asymptotic expansions of solutions for certain classes of systems of integrodifferential equations in a right‐hand neighbourhood of a singular point.

Suggested Citation

  • Zdeněk Šmarda & Yasir Khan, 2012. "Singular Initial Value Problem for a System of Integro‐Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:918281
    DOI: 10.1155/2012/918281
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Donal O'Regan & Oleksandr E. Zernov, 2004. "A singular initial value problem for some functional differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-10, January.
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    Cited by:

    1. Abdon Atangana & Suares Clovis Oukouomi Noutchie, 2014. "Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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