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Kniha popisuje teorii různých prostorů funkcí a dává možnost funkcionálně analytickému přístupu k řešení diferenciálních rovnic. Je rozdělena do tří částí, z nichž první pojednává předběžně o funkcionální analýze, ovektorových, metrických, lineárních, Banachových a Hilbertových prostorech, operátorech apod. Druhá část pojednává o integrovatelných funkcích a o prostorech a integrálech různých autorů. V třetí části se popisují Sobolevovy aOrliczovy prostory, dále prostory anizotropní, Nikolského a Slobodeckého.
In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.
No detailed description available for "Theory of Nonlinear Operators".
No detailed description available for "Theory of Nonlinear Operators".
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Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.
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