Asian Journal of Mathematics and Computer Research

This paper studies the existence of ground state normalized solutions for a modified Kirchhoff equation with the quasilinear term and the Sobolev-Hardy critical exponent. By developing variational methods on the Pohozaev manifold, we prove the existence of solutions for large masses, extending previous results to the challenging case involving the Hardy critical nonlinearity. From a computational perspective, establishing the existence of ground states is crucial for the stability analysis of numerical algorithms used in simulating singular physical systems. Furthermore, the theoretical bounds derived for the mass threshold provide essential constraints for the convergence of iterative schemes in numerical validations.