Existence of solutions of nonlinear m-point boundary-value problems

R Ma, N Castaneda - Journal of Mathematical Analysis and Applications, 2001 - Elsevier
R Ma, N Castaneda
Journal of Mathematical Analysis and Applications, 2001Elsevier
We study the existence of positive solutions to the boundary-value problemu ″+ atfu= 0, t∈
0, 1 x′ 0=∑ i= 1 m− 2 b ix′ ξ i, x 1=∑ i= 1 m− 2 a ix ξ i, where ξi∈(0, 1) with 0< ξ1< ξ2<···<
ξm− 2< 1, ai, bi∈[0,∞) with 0<∑ m− 2i= 1ai< 1, and∑ m− 2i= 1bi< 1. We show the existence
of at least one positive solution if f is either superlinear or sublinear by applying the fixed
point theorem in cones.
We study the existence of positive solutions to the boundary-value problemu″ + a t f u = 0,t ∈ 0, 1 x′ 0 = ∑ i = 1 m − 2 b ix′ ξ i ,x 1 = ∑ i = 1 m − 2 a ix ξ i , where ξi∈(0,1) with 0<ξ12<···<ξm−2<1,ai,bi∈[0,∞) with 0<∑m−2i=1ai<1, and ∑m−2i=1bi<1. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.
Elsevier