Positive solutions for nonlinear m-point boundary value problems of dirichlet type via fixed-point index theory Original Research Article

Let aϵC[0,1], bϵC([0,1], (-∞, 0)). Let φ1(t) be the unique solution of the linear boundary value problem u″(t)+s(t)u′(t)+b(t)u(t)=0, tϵ(0,1) , u(0)=0, u(1)=1 . We study the multiplicity of positive solutions for the m-point boundary value problems of Dirichlet type u″+a(t)u′+b(t)u+g(t)f(u)=0 , View the MathML source , where ξiϵ (0,1) and αiϵ (0, ∞), iϵ {… , m−2), are given constants satisfying Σi=1m−1αiφ1(ξi) < 1. The methods employed are fixed-point index theory.