On a variational statement of a nonlocal boundary value problem for a fourth-order ordinary differential equation
type: Item
instance of: scholarly article
title: On a variational statement of a nonlocal boundary value problem for a fourth-order ordinary differential equation
zbMATH Open document ID: 1183.34020
DOI: 10.1134/S0012266109030045
author: G. B. Lobjanidze
author: Temur Jangveladze
published in: Differential Equations
publication date: 2009-10-08T00:00:00Z
review text: The paper deals with the existence of solutions to a differential equation of the form \[ (k_1(x)u''(x))''-(k_2(x)u'(x))'+k_3(x)u(x)=f(x) \] satisfying the boundary conditions \[ u(-a)=u'(-a)=u'(0)=0\text{ and }\int_{-\xi}^0k_2(x)u'(x)dx-k_1(0)u''(0))+k_1(-\xi)u''(-\xi)=0. \] The authors formulate a minimizing functional defined on an appropriate Hilbert space and then they show that the minimum of the functional is a solution of the original boundary value problem.
reviewed by: George Karakostas
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 5611153
zbMATH Keywords: fourth-order ordinary differential equations
zbMATH Keywords: boundary value problems
zbMATH Keywords: variational methods
Wikidata QID: Q115252758
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5611153