Boundary value problems for fourth order differential equations in Hilbert space
type: Item
instance of: scholarly article
title: Boundary value problems for fourth order differential equations in Hilbert space
zbMATH Open document ID: 0830.34051
DOI: 10.1007/BF02850831
author: D. D. Hai
publication date: 1995-10-22T00:00:00Z
review text: The author proves existence results for two fourth-order non-degenerate two-point boundary value problems considered in real Hilbert space. The differential equation of these boundary value problems has the form \(u^{(IV)}+ f(x, u', u'', u''')= 0\), \(x\in (0, 1)\), where \(f\) satisfies some growth and compactness conditions. Moreover, if some Lipschitz type conditions hold for \(f\), then uniqueness theorems are also given. The author's approach is based on the use of the Leray-Schauder continuation theorem. Note that this paper contains improvements of several results of A. R. Aftabizadeh (1986), C. P. Gupta (1990, 1991), Y. Yang (1988).
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 792938
zbMATH Keywords: fourth-order non-degenerate two-point boundary value problems
zbMATH Keywords: Hilbert space
zbMATH Keywords: uniqueness
reviewed by: A. Filinkov
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 792938