Application of Spectral Methods to Boundary Value Problems for Differential Equations. (7th June 2011)

• Record Type: Journal Article
• Authors: Petronela, Ene
• Other Names: Mantica G. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2011(2011)
• Publication Date: 2011-06-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.5402/2011/276701
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : We try to generalize the concept of a spectrum in the nonlinear case starting from its splitting into several subspectra, not necessarily disjoint, following the classical decomposition of the spectrum. To obtain an extension of spectrum with rich properties, we replace the identity map by a nonlinear operatorJ acting between two Banach spacesX andY, which takes into account the analytical and topological properties of a given operatorF, although the original definitions have been given only in the caseX = Y andJ = I . The FMV spectrum reflects only asymptotic properties ofF, while the Feng's spectrum takes into account the global behaviour ofF and gives applications to boundary value problems for ordinary differential equations or for the second-order differential equations, which are referred to as three-point boundary value problems with the classical or the periodic boundary conditions.