Existence results for $\gamma (\tau )$-triharmonic equation involving Navier boundary conditions and Hardy potential

In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the $\gamma (\tau ) $ -type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this problem under well-structured assumptions. Our approach relies on a novel analytical framework incorporating regularization techniques to handle the non-coercive nature of the $\gamma (\tau ) $ -triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms.