Existence results for γ ( τ ) $γ (τ )$ -triharmonic equation involving Navier boundary conditions and Hardy potential - Abdelaziz Sabiry; Salah Boulaaras; Ali El Mfadel; Rafik Guefaifia (Boundary Value Problems)
Abstract In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the γ ( τ ) $γ (τ ) $ -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 γ ( τ ) $γ (τ ) $ -triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms.