On Volterra type generalization of monotonization method for nonlinear functional operator equations

Solvability of some operator equations and periodic solutions of nonlinear functional differential equations

Journal of Differential Equations ◽

10.1016/0022-0396(83)90004-9 ◽

1983 ◽

Vol 49 (3) ◽

pp. 415-429 ◽

Cited By ~ 6

Author(s):

A Cañada ◽

P Martinez-Amores

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Operator Equations ◽

Nonlinear Functional ◽

Functional Differential

Download Full-text

On a Boundary-Value Problem of Antiperiodic Type for First-Order Nonlinear Functional Differential Equations of Non-Volterra Type

Nonlinear Oscillations ◽

10.1023/b:nono.0000028590.28907.ea ◽

2003 ◽

Vol 6 (4) ◽

pp. 535-559 ◽

Cited By ~ 1

Author(s):

R. Hakl ◽

A. Lomtatidze ◽

J. Šremr

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Boundary Value ◽

Functional Differential Equations ◽

Volterra Type ◽

Nonlinear Functional ◽

First Order ◽

Functional Differential

Download Full-text

Solvability and Bifurcation of Solutions of Nonlinear Equations with Fredholm Operator

Symmetry ◽

10.3390/sym12060912 ◽

2020 ◽

Vol 12 (6) ◽

pp. 912

Author(s):

Nikolai Sidorov ◽

Denis Sidorov ◽

Aliona Dreglea

Keyword(s):

Integral Equations ◽

Nonlinear Operator ◽

Sufficient Conditions ◽

Branch Points ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Nonlinear Functional ◽

Branching Points ◽

Nonstandard Models ◽

Necessary And Sufficient

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.

Download Full-text

Perturbed Integral Operator Equations of Volterra Type with Applications to $${\varvec{p}}$$ p -Laplacian Equations

Mediterranean Journal of Mathematics ◽

10.1007/s00009-018-1090-3 ◽

2018 ◽

Vol 15 (2) ◽

Cited By ~ 1

Author(s):

Christopher S. Goodrich

Keyword(s):

Integral Operator ◽

Volterra Type ◽

Operator Equations ◽

Laplacian Equations

Download Full-text

VOLTERRA FUNCTIONAL-OPERATOR EQUATIONS AND DISTRIBUTED OPTIMIZATION PROBLEMS

Tambov University Reports Series Natural and Technical Sciences ◽

10.20310/1810-0198-2018-23-124-745-756 ◽

2018 ◽

pp. 745-756

Author(s):

Vladimir Iosifovich Sumin

Keyword(s):

Optimization Problems ◽

Initial Boundary ◽

Optimization Methods ◽

Global Solvability ◽

Optimal Controls ◽

Initial Boundary Value Problems ◽

Operator Equations ◽

Functional Operator ◽

Controlled Systems ◽

Initial Boundary Value

A survey of the results obtained in the theory of optimization of distributed systems by the method of Volterra functional-operator equations is given. Topics are considered: the conditions for preserving the global solvability of controllable initial-boundary value problems, optimality conditions, singular controlled systems in the sense of J.L. Lions, singular optimal controls, numerical optimization methods substantiation and others.

Download Full-text

Solvability of Nonlinear Equations in Case of Branching Solutions

10.20944/preprints202004.0288.v1 ◽

2020 ◽

Author(s):

Nikolai A. Sidorov ◽

Denis Sidorov ◽

Aliona Dreglea

Keyword(s):

Integral Equations ◽

Nonlinear Operator ◽

Sufficient Conditions ◽

Branch Points ◽

Operator Equations ◽

Nonlinear Operator Equations ◽

Nonlinear Functional ◽

Branching Points ◽

Nonstandard Models ◽

Necessary And Sufficient

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.

Download Full-text