Abstract
The present research investigates the following delayed problem (0.1)ν′′+a(t)f(t,νt)=0,0<t<1,ν(t)=ϕ(t),−τ≤t≤0,ν′(0)=0,ν(1)=αν(γ)+βν′(γ),0≤γ≤1,0≤ξ<1,0≤υ≤ξ(1−γ),Using kranoselskii fixed point theorem on cones, and the fixed point index theory, we will show the existence of positive solutions for the problem. Also the multiplicity is shown.
•The existence of solution for a second order multi-point delayed boundary value problem.•Multiplicity of solution is achieved.•The kranoselskii fixed point theorem on cones, and the fixed point index theory is used to show the desired result.