Convex Majorants Method in the Theory of Nonlinear Volterra Equations

2011/01/20 by Denis Sidorov, Sidorov, Denis, Nikolay Sidorov +1
Mathematics · #37N35 #45D.04 #93C40 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #G.1.2 #G.1.9 #acm:37N35 #acm:45D.04 #acm:93C40 #math.DS #math.FA #msc:37N35 #msc:45D.04 #msc:93C40

paper · pdf · doi:10.48550/arxiv.1101.3963

arxiv created 2011/01/25 · arxiv updated 2011/01/26

Abstract

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

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