Nonlinear Volterra Equations with Loads and Bifurcation Parameters: Existence Theorems and Construction of Solutions
Abstract: We consider a nonlinear Volterra integral equation with local and/or integral loads on thedesired solution given by the Stieltjes integral. The equation contains a bifurcation parameter andhas the trivial solution for any of the parameter values. Necessary and sufficient conditions areobtained for those values of the parameter (bifurcation points) in the vicinity of which theequation has nontrivial continuous real solutions. The leading terms of the asymptotics of thesolution branches are constructed, and a method for their refinement is indicated. Illustrativeexamples are given. A linearization principle is established that permits one to find bifurcationpoints using only information about the linear part of the nonlinear equation with a vector loadand a vector bifurcation parameter. © 2021, Pleiades Publishing, Ltd.
Библиографическая ссылка
Sidorov N.A., Sidorov D.N. Nonlinear Volterra Equations with Loads and Bifurcation Parameters: Existence Theorems and Construction of Solutions // Differential Equations. Vol.57. №12. 2021. P.1640-1651. DOI: 10.1134/S0012266121120107
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