Open AccessON SOLUTIONS OF ONE 6‐TH ORDER NONLINEAR BOUNDARY VALUE PROBLEM
Author(s) -
Tatjana Garbuza
Publication year - 2008
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/1392-6292.2008.13.349-355
Subject(s) - mathematics , boundary value problem , nonlinear system , order (exchange) , value (mathematics) , mathematical analysis , type (biology) , boundary (topology) , boundary values , pure mathematics , physics , statistics , ecology , finance , quantum mechanics , economics , biology
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.