一类奇异临界双调和椭圆方程的群不变解

On Group-invariant Solutions of a Class of Singular Critical Biharmonic Elliptic Equations

讨论一类含有Hardy-Sobolev临界指数项的奇异双调和椭圆方程,应用Lions集中紧性原理、Palais对称临界原理、Hardy-Rellich型不等式和变分方法,证明了方程在适当条件下群不变解的存在性和多重性.

In this paper, we discuss a class of singular biharmonic elliptic equations with critical Hardy-Sobolev exponent terms. By using the concentration-compactness principle of Lions together with the symmetric criticality principle of Palais,the Hardy-Rellich inequality and variational methods,we prove several existence and multiplicity results of grolap-invari- ant solutions under certain appropriate conditions.