The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (588 KB) | Metadata | Table of Contents | ZAA summary
Volume 10, Issue 2, 1991, pp. 201–204
DOI: 10.4171/ZAA/442

Published online: 1991-06-30

A-Priori Estimates for the Solutions of a Class of Nonlinear Convolution Equations

Sultan N. Askhabov[1] and M.A. Betilgiriev[2]

(1) Checheno-Ingush State University, Grozny, Azerbaidjan
(2) Checheno-Ingush State University, Grozny, Azerbaidjan

We present sharp two-sided a-priori estimates for the solutions of a class of nonlinear Volterra integral equations in the cone of non-negative continuous functions. These estimates enable us to construct a complete metric space which is invariant under the nonlinear convolution operator considered here and to prove that the equation induced by this operator has a unique solution in this space as well as in the class of all non-negative continuous functions vanishing at the origin.

Keywords: Volterra equations, nonlinear equations, non-negative solutions

Askhabov Sultan, Betilgiriev M.A.: A-Priori Estimates for the Solutions of a Class of Nonlinear Convolution Equations. Z. Anal. Anwend. 10 (1991), 201-204. doi: 10.4171/ZAA/442