Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1991-06-30
A-Priori Estimates for the Solutions of a Class of Nonlinear Convolution EquationsSultan N. Askhabov and M.A. Betilgiriev (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