一类奇异椭圆方程无穷多解的存在性

Existence of infinitely many solutions for some singular elliptic equation

研究了有界区域ΩRN上奇异椭圆方程-Δu-μu|x|2=|u|2*(s)-2u|x|s+fλ(x,u)无穷多解的存在性.在f满足非二次条件的情况下,运用对偶喷泉定理证明了存在λ*>0,使得,当λ∈(0,λ*)时,该方程有无穷多个弱解{uk}满足I(uk)<0,并且I(uk)→0,k→+∞.

This paper deals with the existence of infinitely many solutions of the following singular elliptic equation：-Δu-μu｜x｜2=｜u｜2＊（s）-2u｜x｜s＋λf（x,u）.If f satisfies nonquadraticity condition,using variational methods,via dual fountain theorem,proved that there exists there exists λ＊〉0 such that for any λ∈（0,λ＊）,this problem has a sequence of solutions{uk}H10（Ω）such that I（uk）〈0 and I（uk）→0 as k→＋∞.