中国科学院研究生院学报
中國科學院研究生院學報
중국과학원연구생원학보
JOURNAL OF THE GRADUATE SCHOOL OF THE CHINESE ACADEMY OF SCIENCES
2009年
2期
158-166
,共9页
Sobolev临界指数%Hardy位势%山路引理
Sobolev臨界指數%Hardy位勢%山路引理
Sobolev림계지수%Hardy위세%산로인리
critical Sobolev exponents%Hardy potentials%mountain pass lemma
在Rn中具有光滑边界的有界域Ω内考虑具有Dirichlet边界条件的半线性椭圆方程-△u-μu/|x|2=g(x, u) +|u|2*-2u,这里g(x,·)在无穷远处具有次临界增长.由变分法,利用Brézis和Nirenberg"Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents.Comm.Pure Appl.Math.1983,36:437～477"的思想,证明了正解的存在性.
在Rn中具有光滑邊界的有界域Ω內攷慮具有Dirichlet邊界條件的半線性橢圓方程-△u-μu/|x|2=g(x, u) +|u|2*-2u,這裏g(x,·)在無窮遠處具有次臨界增長.由變分法,利用Brézis和Nirenberg"Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents.Comm.Pure Appl.Math.1983,36:437～477"的思想,證明瞭正解的存在性.
재Rn중구유광활변계적유계역Ω내고필구유Dirichlet변계조건적반선성타원방정-△u-μu/|x|2=g(x, u) +|u|2*-2u,저리g(x,·)재무궁원처구유차림계증장.유변분법,이용Brézis화Nirenberg"Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents.Comm.Pure Appl.Math.1983,36:437～477"적사상,증명료정해적존재성.
We consider the following semilinear elliptic equation -△u-μu/|x|2=g(x, u) +|u|2*-2u in Ω with Dirichlet boundary condition, where g (x,·) has subcritical growth at infinity. The existence of positive solutions are obtained by variational method in the spirit of Brézis-Nirenberg.
