Solvability of an Integral Equation of Volterra-Wiener-Hopf Type

Abstract

The paper presents results concerning the solvability of a nonlinear integral equation of Volterra-Stieltjes type. We show that under some assumptions that equation has a continuous and bounded solution defined on the interval $\left[0,\left.\infty \right)\right.$ and having a finite limit at infinity. As a special case of the mentioned integral equation we obtain an integral equation of Volterra-Wiener-Hopf type. That fact enables us to formulate convenient and handy conditions ensuring the solvability of the equation in question in the class of functions defined and continuous on the interval $\left[0,\left.\infty \right)\right.$ and having finite limits at infinity.