两幕喜歌剧《约兰瑟》(Iolanthe),又名《贵族与仙女》(The Peer and the Peri),是英国戏剧作家W.S.吉尔伯特(William Schwenck Gilbert)作曲家与亚瑟·沙利文(Arthur Sullivan)第七次合作,1882年11月25日首演于伦敦萨瓦剧院(Savoy O...两幕喜歌剧《约兰瑟》(Iolanthe),又名《贵族与仙女》(The Peer and the Peri),是英国戏剧作家W.S.吉尔伯特(William Schwenck Gilbert)作曲家与亚瑟·沙利文(Arthur Sullivan)第七次合作,1882年11月25日首演于伦敦萨瓦剧院(Savoy Opera),共演出398场。展开更多
We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−...We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).展开更多
文摘两幕喜歌剧《约兰瑟》(Iolanthe),又名《贵族与仙女》(The Peer and the Peri),是英国戏剧作家W.S.吉尔伯特(William Schwenck Gilbert)作曲家与亚瑟·沙利文(Arthur Sullivan)第七次合作,1882年11月25日首演于伦敦萨瓦剧院(Savoy Opera),共演出398场。
基金supported by the NSFC(11931012,11871387,12371118)。
文摘We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).
