For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy expon...For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy exponent, h(x) ∈ (D^1,2(R^N))^*, the dual space of (D^1,2(R^N)), with h(x)≥(≠)0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if ||h||*〈CN,sAs^N-s/4-2s(1-μ/μ)^1/2, CN,s=4-2s/N-2(N-2/N+2-2s)^N+2-2s/4-2s and As = inf u∈D^1,2(R^N)/{0}∫R^N(|△↓u|^2-μu^2/|x|^2)dx/(∫R^N|u|^2^*(s)/|x|^sdx)^2/2^*(s).展开更多
武汉系统工程学会和武汉市列学技术协会联合主办了“国际沿江城市发展战略讨论会”(ISDSRC'91),从系统工程和系统科学角度来研究城市发展问题。在国际范围内征集论文二百多篇,经会议(程序)学术委员会和组织委员会组织专家评审,...武汉系统工程学会和武汉市列学技术协会联合主办了“国际沿江城市发展战略讨论会”(ISDSRC'91),从系统工程和系统科学角度来研究城市发展问题。在国际范围内征集论文二百多篇,经会议(程序)学术委员会和组织委员会组织专家评审,录用论文155篇,编入会议论文集《城市系统控制工程》(City Systems Control En--gineering)。展开更多
This article considers the equation △2u = f(x,u)with boundary conditions either u|aΩ = au/an|aΩ = 0 or u|aΩ = △u|aΩ = 0, where f(x, t) is asymptotically linear with respect to t at infinity, and Ω is a ...This article considers the equation △2u = f(x,u)with boundary conditions either u|aΩ = au/an|aΩ = 0 or u|aΩ = △u|aΩ = 0, where f(x, t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in R^N, N 〉 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).展开更多
文摘For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy exponent, h(x) ∈ (D^1,2(R^N))^*, the dual space of (D^1,2(R^N)), with h(x)≥(≠)0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if ||h||*〈CN,sAs^N-s/4-2s(1-μ/μ)^1/2, CN,s=4-2s/N-2(N-2/N+2-2s)^N+2-2s/4-2s and As = inf u∈D^1,2(R^N)/{0}∫R^N(|△↓u|^2-μu^2/|x|^2)dx/(∫R^N|u|^2^*(s)/|x|^sdx)^2/2^*(s).
文摘武汉系统工程学会和武汉市列学技术协会联合主办了“国际沿江城市发展战略讨论会”(ISDSRC'91),从系统工程和系统科学角度来研究城市发展问题。在国际范围内征集论文二百多篇,经会议(程序)学术委员会和组织委员会组织专家评审,录用论文155篇,编入会议论文集《城市系统控制工程》(City Systems Control En--gineering)。
基金This work was supported by NSFC(10571174,10631030)and CAS(KJCX3-SYW-S03)
文摘This article considers the equation △2u = f(x,u)with boundary conditions either u|aΩ = au/an|aΩ = 0 or u|aΩ = △u|aΩ = 0, where f(x, t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in R^N, N 〉 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).