The eigenvalue problem and infinitely many sign-changing solutions for an elliptic equation with critical Hardy constant

By Li–Yau's idea and a more precise Hardy's inequality, we obtain a new lower bound of eigenvalues for an elliptic equation with critical Hardy constant. Then using the lower bounds, we prove that there are infinitely many sign-changing solutions for a class of elliptic equation with critical Hardy constant which extends the results in Schechter and Zou (2005) [9] to the critical Hardy constant case.