## Lyapunov-Schmidt Methods in Nonlinear Analysis and ApplicationsThis book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics. The authors expound the recent result on the generalized eigen-value problem, the perturbation method, Schmidt's pseudo-inversion for regularization of linear and nonlinear problems in the branching theory and group methods in bifurcation theory. The book covers regular iterative methods in a neighborhood of branch points and the theory of differential-operator equations with a non-invertible operator in the main expression is constructed. Various recent results on theorems of existence are given including asymptotic, approximate and group methods. The reduction of some mathematics, physics and mechanics problems (capillary-gravity surface wave theory, phase transitions theory, Andronov-Hopf bifurcation, boundary-value problems for the Vlasov-Maxwell system, filtration, magnetic insulation) to operator equations gives rich opportunities for creation and application of stated common methods for which existence theorems and the bifurcation of solutions for these applications are investigated. Audience: The book will be of interest to mathematicians, mechanics, physicists and engineers interested in nonlinear equations and applications to nonlinear and singular systems as well as to researchers and students of these topics. |

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### Contents

II | 1 |

III | 6 |

IV | 14 |

V | 21 |

VI | 28 |

VII | 42 |

VIII | 43 |

IX | 45 |

LVI | 296 |

LVII | 299 |

LIX | 301 |

LX | 302 |

LXI | 306 |

LXII | 311 |

LXIII | 315 |

LXIV | 317 |

X | 50 |

XI | 63 |

XII | 87 |

XIII | 92 |

XIV | 94 |

XV | 99 |

XVI | 103 |

XVII | 121 |

XVIII | 134 |

XIX | 142 |

XX | 149 |

XXI | 151 |

XXII | 152 |

XXIII | 157 |

XXIV | 159 |

XXV | 163 |

XXVI | 168 |

XXVIII | 172 |

XXX | 174 |

XXXI | 178 |

XXXII | 180 |

XXXIII | 183 |

XXXIV | 189 |

XXXV | 195 |

XXXVI | 198 |

XXXVII | 200 |

XXXVIII | 209 |

XXXIX | 213 |

XL | 217 |

XLI | 218 |

XLII | 223 |

XLIII | 226 |

XLV | 232 |

XLVI | 246 |

XLVII | 252 |

XLIX | 256 |

L | 259 |

LI | 270 |

LII | 279 |

LIV | 286 |

LV | 295 |

LXV | 320 |

LXVI | 321 |

LXVII | 323 |

LXVIII | 325 |

LXIX | 328 |

LXX | 330 |

LXXI | 337 |

LXXII | 338 |

LXXIII | 339 |

LXXIV | 343 |

LXXV | 357 |

LXXVI | 362 |

LXXVIII | 364 |

LXXIX | 368 |

LXXX | 373 |

LXXXI | 376 |

LXXXII | 383 |

LXXXV | 393 |

LXXXVI | 397 |

LXXXVII | 404 |

LXXXVIII | 413 |

LXXXIX | 419 |

XCI | 421 |

XCII | 428 |

XCIII | 431 |

XCIV | 434 |

XCV | 435 |

XCVI | 439 |

XCVII | 443 |

XCVIII | 449 |

XCIX | 462 |

C | 468 |

CI | 474 |

CII | 475 |

CIII | 485 |

CIV | 487 |

CV | 497 |

513 | |

### Other editions - View all

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications Nikolay Sidorov,Boris Loginov,A. V. Sinitsyn No preview available - 2014 |

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications Nikolay Sidorov,Boris Loginov,A.V. Sinitsyn,M.V. Falaleev No preview available - 2010 |

### Common terms and phrases

analytic arbitrary assume asymptotics Banach spaces bifurcation points bifurcation theory boundary value problem bounded operator branch point branches of solutions branching theory BSEq closed linear operators coefficients computation conditions of Theorem considered const constant construction continuous functions convergent Corollary corresponding defined Definition differential equations distribution functions domain eigenvalues elements equal equation 0.1 estimation exists formulas Fredholm operator Fredholm point group G group symmetry Hence hold inequality infinitesimal operators initial value problem integral invariant relative inverse lattice Lemma Let the conditions linear operators Loginov manifold matrix moreover neighborhood nonlinear equations obtain operator F operator function parameter perturbation point AQ potential Proof proved real solution reduced regular Remark representation respect root number rotation group satisfied Sidorov singular point small solutions solution of equation subspace Theorem 3.1 trajectory transformations unique solution Vainberg and Trenogin valid VM system zero

### Popular passages

Page 531 - Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Diff.

Page 518 - C. Greengard and PA Raviart, A boundary value problem for the stationary VlasovPoisson equations: The plane diode, Comm. Pure Appl. Math. 43 (1990), 473-507.

Page 543 - Zeidler, E.: [1] Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems, Springer- Verlag, 1985.