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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Abstract

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

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

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1337014661

Digital Object Identifier
doi:10.15352/bjma/1337014661

Mathematical Reviews number (MathSciNet)
MR2862539

Zentralblatt MATH identifier
1246.45004

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

Keywords
Majorants nonlinear Volterra equations successive approximations blow-up branching solution

Citation

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. https://projecteuclid.org/euclid.bjma/1337014661


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References

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