On solutions of one 6‐th order nonlinear boundary value problem

A special technique based on the analysis of oscillatory behaviour of linear equations is applied to investigation of a nonlinear boundary value problem of sixth order. We get the estimation of the number of solutions to boundary value problems of the type x(6) = f(t, x), x(a) = A, x′ (a) = A 1, x″(...

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Bibliographic Details
Main Author: Tatjana Garbuza
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2008-09-01
Series:Mathematical Modelling and Analysis
Subjects:
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/7019
Description
Summary:A special technique based on the analysis of oscillatory behaviour of linear equations is applied to investigation of a nonlinear boundary value problem of sixth order. We get the estimation of the number of solutions to boundary value problems of the type x(6) = f(t, x), x(a) = A, x′ (a) = A 1, x″(a) = A 2, x′″(a) = A 3, x(b) = B, x′(b) = B1 , where f is continuous together with the partial derivative f′x which is supposed to be positive. We assume also that at least one solution of the problem under consideration exists. First Published Online: 14 Oct 2010
ISSN:1392-6292
1648-3510