一类分数阶预定曲率问题多泡解的存在性

Existence of Multi-bubbling Solutions for a Class of Fractional Prescribed Curvature Problems

我们考虑以下分数阶算子预定曲率问题:(-△)^(s)u=K(y)u^(2*s^(-1)),其中N≥3,0s*=2N/N-2s是分数阶临界Sobolev指数,K(y)是一正函数.当K(y)有一列模趋于正无穷大的局部极大值点的条件下,我们利用有限维约化方法,证明了上述问题任意有限个多泡解的存在性.这些解集中在K(y)的k个不同局部极大值点处.

We consider the following prescribed curvature problem of fractional operator:(-△)^(s)u=K(y)u^(2*s^(-1)),where N≥3,0s*=2N/N-2s is the fractional critical Sobolev exponent,K(y)is a positive function.When K(y)has a sequence of strictly local maximum points moving to infinity,we use the finite dimensional reduction method to prove the existence of any finitely many multi-bubbling solutions to the above problem.These solutions concentrate at k different local maximum points of K(y).