Preface |
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.: |
Generalised Jordan chains, sets and root numbers of linear operators |
Regularization of linear equations with Fredholm operators / 2.: |
Principal theorem on regularization of linear equations by the perturbation method / 3.: |
Regularization of linear equations on the basis of perturbation theory in Hilbert spaces / 4.: |
Computation of eigenvalues and eigenvectors of linear operators by pseudo-perturbation method / 5.: |
Notes / 6.: |
Investigation of Bifurcation Points of a Nonlinear Equations |
Lyapunov-Schmidt BEq in the problem of a bifurcation point |
General existence theorems for the bifurcation points |
Construction of asymptotics in a neighborhood of a bifurcation point |
Asymptotic bifurcation points |
On perturbation of the branch points of nonlinear equations |
Notes and generalization |
Regularization of Computation of Solutions in a Neighborhood of the Branch Point |
Construction of the regularizing equation in the problem at a branch point |
Definition and properties of simple solutions |
Regularization of calculations of simple solutions of nonlinear equations |
Regularization of method for continuation along parameter in a neighborhood of a branch point |
Notes and remarks |
Iterations, Interlaced Equations and Lyapunov Convex Majorants in Nonlinear Analysis |
Iterations and uniformization of branching solutions in nonlinear analysis |
BEq and the selection of the initial approximation / 1.1: |
On the role of supporting lines and Newton diagrams in the construction of the initial approximation / 1.2: |
A one-step iteration method / 1.3: |
An N-step iteration method / 1.4: |
On regularization in the sense of Tikhonov, modifications and possible generalizations of an N-step method / 1.5: |
Remarks / 1.6: |
Interlaced and potential BEq |
The property of (S, K)-interlacing of an equation and its inheritance by the BEq / 2.1: |
(T, M)-interlaced and (T[superscript 2], M)-interlaced BEq / 2.2: |
[alpha]-parametric interlaced BEq / 2.3: |
Interlaced BEq of potential type / 2.4: |
Surface bundle of a domain of free parameters / 2.5: |
Parametrization of solutions and the method of successive approximations / 2.6: |
On the role of Lyapunov convex majorants in the nonlocal existence theorems of implicit functions |
Majorants independent of parameters / 3.1: |
Majorants depending on a parameter / 3.2: |
Investigation of the existence domain of the solution of equation F(u, [varepsilon]) = 0. / 3.3: |
Methods of Representation Theory and Group Analysis in Bifurcation Theory |
Nonlinear equations invariant under transformation groups |
Lyapounov-Schmidt BEq and some methods of their reduction |
Some applications |
Hereditary symmetry of branching equations and resolving systems |
Invariance properties of BEq |
Resolving systems for differential equations with Fredholm operator at the derivative and their symmetry |
On the Grobman-Hartman theorem for equations with degenerate operator at the derivative |
Construction and investigation of the branching equation by group analysis methods |
BEq of solutions invariant relative to subgroups of the original equation group symmetry |
Potential BEq |
Direct methods of BEq group invariance usage for its general form construction by admitted group symmetry |
Applications of Lie--Ovsyannikov theorem about invariant manifolds for the construction of BEq general form by allowing group symmetry / 4.1: |
Non-linearly perturbed Helmholtz equations |
Domain symmetry and bifurcational solutions asymptotics / 5.1: |
Periodic solutions / 5.2: |
Capillary--gravity waves in fluid layers |
Capillary--gravity waves in a floating fluid spatial layer / 6.1: |
Capillary--gravity waves at the interface of two fluids flow / 6.2: |
Capillary--gravity waves on a cylindrical surface / 6.3: |
Ferrofluid layer in a magnetic field / 6.4: |
Fluid phase state crystallization problem in statistical crystal theory / 7.: |
The statement of the problem / 7.1: |
Subspaces N(B[subscript s]). Their expansions on irreducible subspaces relative to O[subscript h] / 7.2: |
The BEq construction / 7.3: |
Asymptotics of small solutions families for n[subscript s] = 1, 3 / 7.4: |
Solutions invariant relative to normal divisors O[subscript h] / 7.5: |
Andronov--Hopf bifurcation under group symmetry conditions / 8.: |
BEq derivation in non-stationary bifurcation / 8.1: |
Symmetry inheritance theorem / 8.2: |
BEq construction by group analysis methods / 8.3: |
On the asymptotics of small solutions / 8.4: |
Stability of the bifurcating solutions / 9.: |
Singular Differential Equations in Banach Spaces |
Fundamental operator functions |
Generalized functions in Banach spaces |
Fundamental operator functions of singular differential operators |
Fundamental operator functions of singular integral and integro-differential operators |
The initial value problem for a differential equation having a Noetherian operator at the derivative. Periodic solutions and the property of convergence |
Auxiliary information on Jordan sets of Noetherian operators |
The initial value problem for a linear differential equation |
The initial value problem for a nonlinear differential equation |
Integral pseudo-solutions |
Non-stationary differential equations with singularities |
The initial value problem for a non-stationary linear equation and systems of 1st kind integral Volterra equations |
The initial value problem for a non-stationary linear differential equation and a system of integral Volterra equations with a singularity |
Branching differential equations of the initial value problem with singularity |
The initial value problem for a nonlinear differential equation and equations with a singular point / 3.4: |
Partial differential equations with the Fredholm operator in the main part |
The theory of semigroups and groups of operators with kernels |
Relative resolvents. Relatively adjoint elements |
Relatively spectrally bounded operators and analytical groups of operators with kernells |
Relatively sectorial operators and analytical semigroups of operators with kernels / 5.3: |
Steady-State Solutions of the Vlasov--Maxwell System |
Introduction |
Stationary solutions of a VM system |
The reduction of VM system to the resolving elliptic system (2.28), (2.29) |
The reduction of the resolving system to the unique resolving equation |
Existence of solutions of the boundary value problem (2.40)-(2.42) |
Applications of the reduction theorems |
Normalized solutions for a one-component distribution function |
Non-stationary problem |
Bifurcation points and nontrivial solutions of the stationary VM system |
Statement of the boundary value problem and the problem at a bifurcation point / 4.2: |
Resolution of the bifurcation equation / 4.3: |
The existence theorem for bifurcation points and the construction of asymptotic solutions / 4.4: |
Appendices |
Positive solutions of the nonlinear singular boundary value problem of magnetic insulation / A: |
References |
Preface |
On Regularization of Linear Equations on the Basis of Perturbation Theory / 1.: |
Generalised Jordan chains, sets and root numbers of linear operators |