Nonlinear Biharmonic Equations with Critical Potential

In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub.critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non.singular cases, and we get an interesting result.