Decomposition conditions for two-point boundary value problems
type: Item
instance of: scholarly article
title: Decomposition conditions for two-point boundary value problems
zbMATH Open document ID: 0971.47029
DOI: 10.1155/S0161171200002362
author: Wenying Feng
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-11-04T00:00:00Z
full work available at URL: https://eudml.org/doc/48933
review text: This article deals with Dirichlet, Neumann, periodic and antiperiodic problems for the equation \(x''= f(t,x,x')\). Applying the abstract continuation type theorem of Petryshin on \(A\)-proper mappings the author proves the approximation solvability of the problems listed above; in particular, the classical Galerkin method is justified. It is assumed that the function \(f\) has a form \(f(t,x,p)= g(t,x,p)+ h(t,x,p)\), where \(g(t,x,p)\) satisfies conditions which garantee the nonnegativity of integrals \(\int^1_0 xg(t,x,p) dt\) for corresponding subspace of \(C^2([0,1])\), and \(h(t,x,p)\) satisfies inequalities of type \(|h(t,x,p)|\leq a|x|+ b|p|\) with suitable \(a> 0\), \(b>0\).
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 1548205
zbMATH Keywords: Dirichlet, Neumann, periodic and antiperiodic problems
zbMATH Keywords: \(A\)-proper mappings
zbMATH Keywords: approximation solvability
zbMATH Keywords: Galerkin method
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
OpenAlex ID: W2026948555
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description: scientific article; zbMATH DE number 1548205