Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberga€?s model type

摘要

In this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberga€?s model type, this last arises in growing cell populations. The entries of block operator matrix associated to this system are nonlinear and act on the Banach space X p:= L p([0, 1] ?— [a, b]; d?μ dv), where 0 a‰¤ a b a??; 1 p a??.