Well-posedness of solution for a second-order boundary value problem with delay

Abstract

We are concerned in this research to study a singular delayed boundary value problem that is expressed in the form We are concerned in this research to study a singular delayed boundary value problem that is expressed in the form \begin{equation} \left\{ \begin{array}{lll} v^{\prime \prime }+r(t)f(v_{t})=0. & 0<t<1, &  \\ v(t)=\phi (t) & -\tau \leq t\ \leq 0 &  \\ v^{\prime }(0)=0 & v(1)=\e v(\kappa )+\rho v^{\prime }(1) & \end{array}% \right.  \label{PB P} \end{equation} This article shows the analyse for  solution of the singular delayed boundary value problem, where the fixed point theorem on cones is utilized to show this result. Moreover, the multiplicity of solutions is also achieved.