Solvability and bifurcation of solutions of nonlinear equations with fredholm operator
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 ofKronecker-Poincare, Morse-Conley index, power geometry and othermethods are employed. Proposedmethodology 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 proposedmethods are illustrated on the nonlinear integral equations. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
Библиографическая ссылка
Sidorov N., Sidorov D., Dreglea A. Solvability and bifurcation of solutions of nonlinear equations with fredholm operator // Symmetry. Vol.12. No.6. ID: 912. 2020. DOI: 10.3390/SYM12060912
