THREE POSITIVE SOLUTIONS FOR A GENERALIZED STURM-LIOUVILLE MULTIPOINT BVP WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE

TitleTHREE POSITIVE SOLUTIONS FOR A GENERALIZED STURM-LIOUVILLE MULTIPOINT BVP WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE
Publication TypeJournal Article
Year of Publication2008
AuthorsZHANG YOU-WEI, SUN HONG-RUI
JournalDynamic Systems and Applications
Volume17
Start Page313
Pagination12
Date Published2008
ISSN1056-2176
AMS Subject Classification34B15, 39A10
Abstract

In this paper, we are concerned with the following generalized Sturm-Liouville multipoint boundary value problem u 00(t) + h (t) f (t, u (t), u 0 (t)) = 0, 0 < t < 1, au (0) − bu0 (0) = mX−2 i=1 aiu(ξi), cu (1) + du0 (1) = mX−2 i=1 biu(ξi), where 0 < ξ1 < · · · < ξm−2 < 1 (m ≥ 3), a, b, c, d ∈ [0, ∞), ai , bi ∈ (0, ∞) (i = 1, 2, . . . , m − 2) are constants satisfying some suitable conditions. Existence criteria for at least three positive solutions are established by using the fixed point theorem of Avery and Peterson. The interesting point is the nonlinear term f which is involved with the first order derivative explicitly.

PDFhttps://acadsol.eu/dsa/articles/17/DSA-2007-313-324.pdf
Refereed DesignationRefereed