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

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