Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Solvability of Nonlinear Equations in Case of Branching Solutions

Version 1 : Received: 16 April 2020 / Approved: 17 April 2020 / Online: 17 April 2020 (01:34:37 CEST)

A peer-reviewed article of this Preprint also exists.

A. Sidorov, N.; Sidorov, D.; Dreglea, A.I. Solvability and Bifurcation of Solutions of Nonlinear Equations with Fredholm Operator. Symmetry 2020, 12, 912. A. Sidorov, N.; Sidorov, D.; Dreglea, A.I. Solvability and Bifurcation of Solutions of Nonlinear Equations with Fredholm Operator. Symmetry 2020, 12, 912.

Journal reference: Symmetry 2020, 12, 912
DOI: 10.3390/sym12060912

Abstract

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

Subject Areas

branch points; bifurcation points; Fredholm operator; uniformization; asymptotics; iterations; regularization

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.