Bootstrapping and fixed point techniques for the existence of solutions to iterative nonlinear elliptic systems

We make several discoveries about the existence of positive radial solutions (PRSs) to the iterative system of nonlinear elliptic equations (ISNEEqs) coupled with one of the sets of boundary conditions in an annulus via a variety of fixed point theorems (FPTs) on suitable cones in Banach spaces. Specific subsequent outcomes are achieved. On top of that, this work utilizes Rus's theorem in a metric space to derive the necessary criteria for establishing the existence of unique PRS for the system. The novel part of this research is how using the bootstrapping argument together with various fixed point techniques, such findings are attained for the proposed problem. We provide illustrations of how the most significant discoveries might be put into practice in order to show the importance of our findings.