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1.

図書

図書
Kiyohiro Ikeda, Kazuo Murota
出版情報: New York : Springer, c2002  xvii, 411 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 149
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2.

図書

図書
Boris Buffoni and John Toland
出版情報: Princeton, N.J. ; Woodstock : Princeton University Press, c2003  x, 169 p. ; 24 cm
シリーズ名: Princeton series in applied mathematics
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3.

図書

図書
Yuri A. Kuznetsov
出版情報: New York ; Tokyo : Springer, c2004  xxii, 631 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 112
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4.

図書

図書
Alexander D. Bazykin ; edited by Alexander I. Khibnik, Bernd Krauskopf
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1998  xxi, 193 p. ; 26 cm
シリーズ名: World Scientific series on nonlinear science / editor, Leon O. Chua ; ser. A . Monographs and treatises ; v. 11
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5.

図書

図書
edited by Guanrong Chen
出版情報: Boca Raton, FL : CRC Press, c2000  xvii, 648 p. ; 24 cm
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6.

図書

図書
Eusebius Doedel, Laurette S. Tuckerman, editors
出版情報: New York : Springer, c2000  x, 471 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 119
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7.

図書

図書
Hansjörg Kielhöfer
出版情報: New York : Springer, c2004  vii, 346 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 156
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8.

図書

図書
by Nikolay Sidorov ... [et al.]
出版情報: Dordrecht ; London : Kluwer Academic Publishers, c2002  xx, 548 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 550
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目次情報: 続きを見る
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
9.

図書

図書
Yu. Ilyashenko, Weigu Li
出版情報: Providence, R.I. : American Mathematical Society, c1999  xiii, 286 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 66
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目次情報: 続きを見る
Introduction
Preliminaries Bifurcations in the plane
Homoclinic orbits of nonhyperbolic singular points
Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case
Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case
Bifurcations of homoclinic trajectories of hyperbolic saddles
Elements of hyperbolic theory Normal forms for local families: Hyperbolic case
Normal forms for unfoldings of saddlenodes
Bibliography
Introduction
Preliminaries Bifurcations in the plane
Homoclinic orbits of nonhyperbolic singular points
10.

図書

図書
Rüdiger Seydel
出版情報: New York : Elsevier, c1988  xv, 367 p. ; 24 cm
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