Boundary value problem for an infinite system of second order differential equations in $\ell_p$ spaces

The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in $\ell_p$ space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo's type fixed point theorem. The result is illustrated with help of an example.