• Nie Znaleziono Wyników

Control and Cybernetics

N/A
N/A
Info
Pobierz
Protected

Academic year: 2021

Share "Control and Cybernetics"

Copied!
2
0
0

Ładowanie.... (Zobacz pełny tekst teraz)

Pobierz teraz ( 2 Stron )

Pełen tekst

(1)

Control and Cybernetics

vol. 36 (2007) No. 4

Book review:

METHODS OF NONLINEAR ANALYSIS. Applications to Differential Equations

by

Pavel Drábek, Jaroslav Milota

The book “Methods of Nonlinear Analysis, Applications to Differential Equa- tions” by Pavel Drábek, Jaroslav Milota – the known Czech mathematicians – is devoted to methods of nonlinear analysis and their applications. In view of the fact that the real-world problems are in essence nonlinear, the methods of nonlinear analysis became important tools of modern mathematical modelling.

The book introduces fundamental methods of nonlinear analysis, explains them in a general framework, and illustrates on simple examples, typically on boundary value problems for elementary ordinary or partial differential equa- tions.

The exposition of the material is at two levels: a self-contained basic level and an advanced level contained in several appendices.

The basic material includes in particular:

• main tools from linear algebra and linear functional analysis,

• compact operators, contraction principle,

• differential and integral calculus in normed linear spaces,

• inverse function theorem, implicit function theorem, rank theorem, local bifurcation theorem of Crandall and Rabinowitz,

• topological and monotonicity methods of nonlinear analysis, the Brouwer and Schauder fixed point theorems, the method of monotone iterations based on the notions of super-and sub-solutions,

• variational methods, method of Lagrange multipliers, the mountain pass theorem,

• applications of the presented methods to boundary value problems for elementary nonlinear partial differential equations.

Owing to a comprehensive presentation of a broad range of methods of non- linear analysis with clear exposition of their applications to differential equations the book is a very valuable position in the field of applied mathematics.

Irena Pawłow

(2)

1048

I. PAWŁOW

Pavel Drábek, Jaroslav Milota, Methods of Nonlinear Analysis. Applica-

tions to Differential Equations. Birkhäuser Verlag AG, Basel-Boston-Berlin,

2007, 568 pages, ISBN 13-978-3-8146-2. Price (hardcover): 69.90 EUR.

Cytaty

Pobierz teraz ( PDF - 2 Stron - 41.30 KB )

Powiązane dokumenty

Simplified methods applied to nonlinear motion of spar platforms

nonlinear effects which are not included here could also be important, such as: off-diagonal second order pitch excitation, wind excitation, nonlinear mooring restoring forces,

Siloksany w biogazie

Podczas spalania biogazu z odpadów zawierających siloksany uwalniany jest krzem, który może łączyć się z tlenem lub różnymi innymi pierwiastkami w

Nonconvulsive epileptic seizure monitoring with incremental learning

These approaches differ in the way they reduce the set of potentially available support vectors (i.e. training samples) that are used to build the decision function of the

Prawne implikacje obowiązku podatnika prowadzenia ksiąg

Ustawa z 19 grudnia 1980 r. 486) nie przewiduje jakiejkol­ wiek formy czy sposobu odtwarzania ksiąg podatkowych lub urządzeń księgo­ wych. 496) nakłada na podat­

Applications of Nonlinear Perturbation Theory to the Existence of Methods of Lines for Functional Evolutions in Reflexive Banach Spaces

In order to apply Lemma A to this problem, we notice again that the term in H(t,x) after the minus sign is a Lipschitz continuous function on X with Lipschitz constant

To get familiar with the methodology of control systems simulations in Mathematica, methods for results visualization and analysis.

¶ The system equations in this form, together with all the accompanying matrices and vectors are defined in the Mathematica notebook file, provided on the course web page in

1. The hybrid procedure. Let us consider the system of linear equa- tions

It seems quite difficult to obtain more theoretical results on the convergence of the hybrid procedure in the general case... It was introduced in [6, 7] and applied to some well

to nonlinear differen al equa ons of the second order

Mustafa, On the existence of solu ons with prescribed asympto c behaviour for perturbed non- linear differen al equa ons of second order, Glasgow Math. Saker, Boundedness of solu