Banach Journal of Mathematical Analysis

Convex majorants method in the theory of nonlinear Volterra equations

Denis N. Sidorov and Nikolai A. Sidorov

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The main solutions in the sense of Kantorovich of nonlinear Volterra operator-integral equations are constructed. Convergence of the successive approximation method is established through studies of the majorant integral equations and the majorant algebraic equations. Estimates are derived for the solutions and for the intervals on the right margin of which the solution of nonlinear Volterra operator-integral equation has blow-up or solution start branching.

Article information

Banach J. Math. Anal., Volume 6, Number 1 (2012), 1-10.

First available in Project Euclid: 14 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 93C40: Adaptive control 49J22

Majorants nonlinear Volterra equations successive approximations blow-up branching solution


Sidorov , Denis N.; Sidorov , Nikolai A. Convex majorants method in the theory of nonlinear Volterra equations. Banach J. Math. Anal. 6 (2012), no. 1, 1--10. doi:10.15352/bjma/1337014661.

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