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

In this manuscript, we introduce and study the existence of solutions for a coupled system of differential equations under abstract boundary conditions of Rotenberg’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 Xp:= Lp([0, 1] × [a, b]; dµ dv), where 0 ≤ a < b < ∞; 1 < p < ∞.