Multiple positive solutions of fourth-order four-point boundary-value problems with changing sign coefficient

In this paper, we investigate the existence of multiple positive solutions of the fourth-order four-point boundary-value problems $$displaylines{ y^{(4)}(t) = h(t) g(y(t), y''(t)), quad 0 < t < 1, cr y(0) = y(1) = 0, cr a y''(xi_1)-b y'''(xi_1) = 0, qu...

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Bibliographic Details
Main Authors: Chuanzhi Bai, Chunhong Li, Zheng Fang
Format: Article
Language:English
Published: Texas State University 2008-12-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2008/159/abstr.html
Description
Summary:In this paper, we investigate the existence of multiple positive solutions of the fourth-order four-point boundary-value problems $$displaylines{ y^{(4)}(t) = h(t) g(y(t), y''(t)), quad 0 < t < 1, cr y(0) = y(1) = 0, cr a y''(xi_1)-b y'''(xi_1) = 0, quad c y''(xi_2)+d y'''(xi_2) = 0, }$$ where $0 < xi_1 < xi_2 < 1$. We show the existence of three positive solutions by applying the Avery and Peterson fixed point theorem in a cone, here $h(t)$ may change sign on $[0, 1]$.
ISSN:1072-6691