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
2010年
3期
306-313
,共8页
Hardy-Sobolev临界指数%半线性椭圆方程%环绕定理%非平凡解
Hardy-Sobolev臨界指數%半線性橢圓方程%環繞定理%非平凡解
Hardy-Sobolev림계지수%반선성타원방정%배요정리%비평범해
Hardy-Sobolev critical exponent%semilinear elliptic equation%linking theorem%nontrivial solution
借助环绕定理和非线性分析技巧,研究如下一类带Hardy-Sobolev临界指数和权函数的半线性椭圆方程{-△u-μ(u/|x|=λu+K(x)(|u|2*(s)-2u/|x|s,x∈Ω;u=0,x∈(ζ)Ω)),解的存在性,其中Ω是RN具有光滑边界的有界开区域,0∈Ω,N≥5,0≤s≤2,0≤μ≤((N-2)/2)2,λ＞0,K(χ)是Ω上有界正函数.
藉助環繞定理和非線性分析技巧,研究如下一類帶Hardy-Sobolev臨界指數和權函數的半線性橢圓方程{-△u-μ(u/|x|=λu+K(x)(|u|2*(s)-2u/|x|s,x∈Ω;u=0,x∈(ζ)Ω)),解的存在性,其中Ω是RN具有光滑邊界的有界開區域,0∈Ω,N≥5,0≤s≤2,0≤μ≤((N-2)/2)2,λ＞0,K(χ)是Ω上有界正函數.
차조배요정리화비선성분석기교,연구여하일류대Hardy-Sobolev림계지수화권함수적반선성타원방정{-△u-μ(u/|x|=λu+K(x)(|u|2*(s)-2u/|x|s,x∈Ω;u=0,x∈(ζ)Ω)),해적존재성,기중Ω시RN구유광활변계적유계개구역,0∈Ω,N≥5,0≤s≤2,0≤μ≤((N-2)/2)2,λ＞0,K(χ)시Ω상유계정함수.
Abstract Using linking theorem and analytic technique, we discuss the existence of nontrivial solutions for the following semilinear elliptic problem with Hardy-Sobolev critical exponents and weights{-△u-μ(u/|x|=λu+K(x)(|u|2*(s)-2u/|x|s,x∈Ω;u=0,x∈(ζ)Ω)),where Ω is an open bounded domain of RN with smooth boundary (ζ)Ω and 0∈Ω,N≥5,0≤s≤2,0≤μ≤((n-2)/2)2,λ＞0,and K(χ)is a bounded positive function on Ω.
