Pohozaev Identities For Elliptic Equations And Applications

In this paper, we consider the Pohozaev identities for several kinds of elliptic equations. Especially, we derive the Pohozaev identity for p-harmonic equation from which we obtain the corresponding nonexistence of nontrivial solution for p-harmonic equation with critical growth.Firstly, we introduce the researching situation about Pohozaev identities and their applications. Then we derive the identities for several kinds of common elliptic operators by the method, which is different from the universal approach that the identities derived from the introduction. At last, in Section 3, we calculate the Pohozaev identity for p-harmonic equation under Navier or Dirichlet boundary condition from which we obtain the corresponding nonexistence of nontrivial solutions for p-harmonic equations with critical growth.