Positive Solutions of a Singular Third-Order m-Point Boundary Value Problem

Abstract

This paper is concerned with the existence and nonexistence of positive solutions to the singular third-order m-point boundary value problem u′′′(t)+a(t)f(u(t))=0, 0<t<1, u(0)=u'(0)=0, u'(1)-∑i=1m-2αiu'(ξi)=λ, where ξi∈[0,1), αi∈[0,∞) (i=1,2,…,m-2) are constants, λ∈(0,1) is a parameter, f:[0,∞)→[0,∞) is continuous and a(·) is allowed to be singular at t=0 and t=1. The results here essentially extend and improve some known results.