Study of a Lane-Emden type equation under Navier boundary conditions and topological insight using persistent homology

Abstract

In this paper, we investigate a Lane-Emden type equation under Navier boundary conditions. Under a given set of assumptions, we prove the existence and uniqueness of a weak solution to the problem using variational methods. Subsequently, we use persistent homology to analyze the topological features of the solution and to track the behavior of its critical points, capturing their birth, death, and structural persistence across multiple scales.