具有临界指数的双调和方程的非平凡解的存在性

The Existence of Nontrival solutions of Biharmonic Equation Involving ChiticalExponent

研究了Ｒ￣Ｎ上具有临界Ｓｏｂｏｌｅｖ指数的双调和方程，且非平凡解的存在性．这里ａ（ｘ）≥０且；应用形变引理和拓扑度方法证明了当充分小时，上述方程至少有一个不变号的非平凡解．

The existence of non-trivialsolutin of the biharmonic equation with critical exponent△￣(2)u+a(x)u=|u|￣(2￣*-2)u inR￣N,and was investigated.Here and,N≥5,2￣(*)=2N/(N-4).It has been proven that the above equation has at least one non-trivial solution which do notchange sign in R￣N if is small enough by means of deformation lemma and the method oftopological degree.