ABSTRACT In this paper, we consider a class of fourth‐order singular boundary value problems (BVPs) that arise in the semiconductor industry. We present explicit results on the existence of solutions to the governing nonlinear fourth‐order model, which represents an advancement over the theoretical and numerical results in the literature. The governing problem is formulated over a disk‐shaped domain with an arbitrary radius . Due to the presence of a nonself‐adjoint operator, singular behavior at the origin, nonlinearity, and higher‐order terms, the analysis of the radial problem poses significant theoretical and numerical challenges. We first investigate the sign of the solutions. To establish the existence of at least one solution in a continuous function space, we employ the monotone iterative method tailored to the associated radial system. Furthermore, we also identify precise limits for the parameter beyond which the problem admits no solutions. We verify the theoretical findings with existing numerical results. This study demonstrates its effectiveness by establishing several crucial results applicable for arbitrary radius , , and a varying deposition function .
Manini et al. (2026) studied this question.