On a Homogeneous Integral Equation with Two Kernels

Abstract

The present paper is devoted to the finding conditions of nontrivial (non-zero) solvability of some classes of equations of the form \(S\left( x \right) = \int_0^\infty {{T_1}\left( {x - t} \right)S\left( t \right)} dt + \int_{ - \infty }^0 {{T_2}\left( {x - t} \right)S\left( t \right)} dt\), x ∈ R, with respect to unknown function S. The asymptotic behavior of the solution S is also studied.