<abstract xmlns="http://www.w3.org/1999/xhtml"> Without solving the linear Volterra integral equation of the form <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/awutm-2013-0009_1"></inline-graphic></inline-formula> with unit source term and convolution kernel, some properties of the solution such as the number of zeroes, positivity, boundedness and monotonicity were obtained in [6] for t∈[0,∞] by usage of [4], the Equivalence Theorem and Convolution Theorem which are given, below. Also, the boundaries |h(t)|≤2, |h(t)|≤22 and |h(t)|≤2n, (n∈ℕ) for the solution of this equation were found, [7, 9, 10]. The boundaries for functions h',h'',...,h(n), n∈ℕ defined on the infinite interval [0;1) were obtained in [11,12]. Some properties of the solution of the integral equation of the form f(t)=ɸ(t) which is more general than the previous equation are investigated on the infinite interval, [8]. In the present work, it is shown that some results different than that of [8] can be derived for an Volterra equation of the form f(t)=ɸ(t)-K∗f </abstract>

Without solving the linear Volterra integral equation of the form  with unit source term and convolution kernel, some properties of the solution such as the number of zeroes, positivity, boundedness and monotonicity were obtained in [6] for t∈[0,∞] by usage of [4], the Equivalence Theorem and Convolution Theorem which are given, below. Also, the boundaries |h(t)|≤2, |h(t)|≤22  and |h(t)|≤2n, (n∈ℕ) for the solution of this equation were found, [7, 9, 10]. The boundaries for functions h',h'',...,h(n), n∈ℕ defined on the infinite interval [0;1) were obtained in [11,12]. Some properties of the solution of the integral equation of the form f(t)=ɸ(t) which is more general than the previous equation are investigated on the infinite interval, [8]. In the present work, it is shown that some results different than that of [8] can be derived for an Volterra equation of the form f(t)=ɸ(t)-K∗f

On Some Properties of the Solution of the Linear Integral Equation of Volterra Type

Inönü Üniversitesi Egitim Fakültesi 44280-Malatya Turkey

Annals of West University of Timisoara - Mathematics and Computer Science

Without solving the linear Volterra integral equation of the form  with unit source term and convolution kernel, some properties of the solution such as the...

On Some Properties of the Solution of the Linear Integral Equation of Volterra Type

Published Online: Aug 14, 2013

Page range: 117 - 151

DOI: https://doi.org/10.2478/awutm-2013-0009

Keywords
Linear Volterra integral equations with convolution kernel, Convolution theorem

This content is open access.

On Some Properties of the Solution of the Linear Integral Equation of Volterra Type

Published Online: Aug 14, 2013

Page range: 117 - 151

DOI: https://doi.org/10.2478/awutm-2013-0009

KeywordsLinear Volterra integral equations with convolution kernel, Convolution theorem

This content is open access.

Keywords
Linear Volterra integral equations with convolution kernel, Convolution theorem