Articoli correlati a Integral operators in spaces of summable functions:...

Integral operators in spaces of summable functions: 1 - Brossura

Krasnosel'skii, M.A.; Zabreyko, P.P.; Pustylnik, E.I.; Sobolevski, P.E.

 
9789401015448: Integral operators in spaces of summable functions: 1
Brossura
ISBN 10: 9401015449 ISBN 13: 9789401015448
Casa editrice: Springer, 2011

Sinossi

The investigation of many mathematical problems is significantly simplified if it is possible to reduce them to equations involving continuous or com­ pletely continuous operators in function spaces. In particular, this is true for non-linear boundary value problems and for integro-differential and integral equations. To effect a transformation to equations with continuous or completely continuous operators, it is usually necessary to reduce the original problem to one involving integral equations. Here, negative and fractional powers of those unbounded differential operators which constitute 'principal parts' of the original problem, are used in an essential way. Next there is chosen or constructed a function space in which the corresponding integral oper­ ator possesses sufficiently good properties. Once such a space is found, the original problem can often be analyzed by applying general theorems (Fredholm theorems in the study of linear equations, fixed point principles in the study of non-linear equations, methods of the theory of cones in the study of positive solutions, etc.). In other words, the investigation of many problems is effectively divided into three independent parts: transformation to an integral equation, investi­ gation of the corresponding integral expression as an operator acting in function spaces, and, finally, application of general methods of functional analysis to the investigation of the linear and non-linear equations.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Dalla quarta di copertina

The investigation of many mathematical problems is significantly simplified if it is possible to reduce them to equations involving continuous or com­ pletely continuous operators in function spaces. In particular, this is true for non-linear boundary value problems and for integro-differential and integral equations. To effect a transformation to equations with continuous or completely continuous operators, it is usually necessary to reduce the original problem to one involving integral equations. Here, negative and fractional powers of those unbounded differential operators which constitute 'principal parts' of the original problem, are used in an essential way. Next there is chosen or constructed a function space in which the corresponding integral oper­ ator possesses sufficiently good properties. Once such a space is found, the original problem can often be analyzed by applying general theorems (Fredholm theorems in the study of linear equations, fixed point principles in the study of non-linear equations, methods of the theory of cones in the study of positive solutions, etc.). In other words, the investigation of many problems is effectively divided into three independent parts: transformation to an integral equation, investi­ gation of the corresponding integral expression as an operator acting in function spaces, and, finally, application of general methods of functional analysis to the investigation of the linear and non-linear equations.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer
Data di pubblicazione
2011
Lingua
Inglese
ISBN 10 
9401015449
ISBN 13 
9789401015448
Rilegatura
Copertina flessibile
Numero di pagine
536
Contatto del produttore
ProductSafety@springernature.com
ProductSafety@springernature.com

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