一类临界位势非线性椭圆型方程非平凡解的存在性

Existence of nontrivial solutions of nonlinear elliptic equation with critical potential

建立了一个新的Hilbert空间H,在新的空间中讨论四维临界位势的非线性椭圆型方程,利用山路引理和(PS)条件,证明了方程非平凡解的存在性。

Through the establishment of a new space H, the existence of nontrivial solutions of fourth-order nonlinear elliptic equation with critical potential in the new Hilbert space are discussed. It proves the existence problem of nontrivial solution in this new space by using the Mountain pass theorem and the （PS） condition.