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

Abstract: In this paper the concept of measure of noncompactness is applied to prove the existence of 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 obtain the result for the system of integral equations, using Darbo type fixed point theorem. The result is applied to an example to illustrate the concept.