Loading...
Please wait, while we are loading the content...
Similar Documents
Solvability and Bifurcation of Solutions of Nonlinear Equations with Fredholm Operator
| Content Provider | MDPI |
|---|---|
| Author | Sidorov, Nikolai Sidorov, Denis Dreglea, Aliona |
| Copyright Year | 2020 |
| Description | 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 the reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincaré, 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 and effectiveness of the proposed methods are illustrated on the nonlinear integral equations. |
| Starting Page | 912 |
| e-ISSN | 20738994 |
| DOI | 10.3390/sym12060912 |
| Journal | Symmetry |
| Issue Number | 6 |
| Volume Number | 12 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2020-06-01 |
| Access Restriction | Open |
| Subject Keyword | Symmetry Automotive Engineering Mathematical Physics Branch Points Bifurcation Points Fredholm Operator Uniformization Asymptotics Iterations Regularization |
| Content Type | Text |
| Resource Type | Article |
