一个新Pohozaev恒等式及其在四阶拟线性椭圆方程中的应用

对于具有Dirichlet边界条件的四阶p-双调和椭圆方程,建立了一个新的Pohozaev恒等式.利用该恒等式,得到了两类拟线性问题弱解不存在的充分性条件.最后,还讨论了具有Navier边界条件的p-双调和问题的Pohozaev恒等式.研究结果将对研究某些类p-双调和方程解的非存在性起到很好的作用.

New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation

For fourth order p-biharmonic elliptic equation with Dirichlet boundary conditions,a new Pohozaev type identity is established.In view of the identity,the sufficient conditions of nonexistence of weak solution for two classes of quasilinear probles are obtained.The Pohozaev type identity for p-biharmonic problem with Navier boundary conditions is discussed.These results exhibit the significance for nonexistence of solution of p-biharmonic problem.