Existence and Nonexistence of Radial Solutions for a Class of Fourth‐Order Systems of Elliptic PDEs

ABSTRACT

In this work, we propose a nonlinear fourth‐order system of elliptic partial differential equations as follows: where the constants , , , and satisfy the relation The parameters and are real, and and denote the deposition rates of the incoming particles. The parameters and satisfy where and are the critical values of and , respectively. We investigate the system of radial solutions of the governing coupled PDEs. Since the radial system involves a nonself‐adjoint operator, exhibits a singularity at the origin, and is nonlinear and of higher order, it is difficult to analyze both theoretically and numerically. In this work, we determine the sign of the radial solutions. We apply the monotone iterative method to the associated radial problem to establish the existence of at least one solution in a continuous space. We also compute the parameter ranges for and for which the nonexistence of solutions is guaranteed. To obtain approximate solutions, we develop an iterative scheme and provide numerical results to validate the theoretical findings.