On Nonlinear Volterra Equations with Nonintegrable Kernels

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1980 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 11, pages 668-682 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Gripenberg, Gustaf;

doi: 10.1137/0511062

On Nonlinear Volterra Equations with Nonintegrable Kernels

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Abstract

In this paper, the asymptotic behavior of solutions of the nonlinear real Volterra equation \[x(t) + \int_0^t {g(x(t - s))a(s)ds = f(t),\quad t \geqq 0} \] is studied. Here a and f are given and x is the unknown function. The assumptions on the function f are rather weak, and in most cases it is assumed that $\int _0^\infty a(s)ds = + \infty $.

Keywords

Other nonlinear integral equations, bounded solution, Volterra integral equations, asymptotic behavior, Asymptotics of solutions to integral equations

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