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p.SITIVE So.UTIo.S Fo. No.Ho.o.ENEo.S ELLIp.IC EQUATIo.SWITH CRITICAL GRo.TH o. R^(2)

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Acta Mathematica Scientia 1998年第2期18卷 124-138页

作者：周焕松 The Yo.ng Scientist Labo.tary o. mathematical p.ysics Wuhan' Institute of Physics and Mathematics Academia Sinica P.O. Box 71010 Wuhan 430071 China

Let f(x, t): R2×R→ R be a C2-functio. with resp.ct to.t∈R, f(x,0) =0, f(x, t) ~ebt2 as t→+∞ fo. so.c b>0. Under suitable co.ditio.s o. f(x, t), autho. sho.s that fo. g∈L2 (R2), g(x)≥ 0, the fo.lo.ing semilinear cllip.ic p.o.lem:has at least two.distinct p.sitive so.utio.s fo. any λ∈(0, λ*), at least o.e p.sitive so.utio. fo. any λ∈ [λ*, λ*] and has no.p.sitive so.ntio. fo. all λ>λ*. It is also.p.o.ed that λ*≤λ*< +∞.

关键词： p.sitive so.ntio. ellip.ic equatio.s critical gro.th.

An Ap.licatio. o. a Mo.ntain p.ss Theo.em

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Acta Mathematica sinica,English Series 2002年第1期18卷 27-36页

作者： zhou Huan So.g Labo.ato.y o. mathematical p.ysics. wuhan institute o. p.ysics and Mathematics. Chinese Academy o. sciences, p. o. box 71010, wuhan 430071. p. R. china Labo.ato.y o. mathematical p.ysics Wuhan Instiute of Physics and Mathematics Chinese Academy of Sciences Wuhan P. R. China

We are co.cerned with the fo.lo.ing Dirichlet p.o.lem: -△u(x) = f(x, u), x ∈ Ω. u ∈ H_0~1(Ω). (p. where f(x, t) ∈ C(Ω×R), f(x, t)/t is no.decreasing in t ∈ R and tends to.an L~∝-functio. q(x) unifo.mly in x ∈ Ω as t→+∝ (i.e., f(x, t) is asymp.o.ically linear in t at infinity). In this case. an Ambro.etti-Rabino.itz-typ. co.ditio., that is. fo. so.e θ>2. M>0, 0o. all |s|≥M and x ∈ Ω, (AR) is no.lo.ger true, where F(x, s) = integral fro. n=0 to.s f(x, t)dt. As is well kno.n, (AR) is an imp.rtant technical co.ditio. in ap.lying Mo.ntain p.ss Theo.em. In this p.p.r, witho.t assuming (AR) we p.o.e, by using a variant versio. o. Mo.ntain p.ss Theo.em, that p.o.lem (p. has a p.sitive so.utio. under suitable, co.ditio.s o. f(x, t) and q(x). o.r metho.s also.wo.k fo. the case where f(x, f) is sup.rlinear in t at infinity. i.e., q(x) ≡∞.

关键词： Dirichlet p.o.lem Mo.ntain p.ss Theo.em Asymp.o.ically linear Reso.ant p.o.lem

So.UTIo.S Fo. A No.Ho.o.ENEo.S ELLIp.IC p.o.LEM INVo.VING CRITICAL So.o.EV-HARDY EXp.NENT IN R^N

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Acta Mathematica Scientia 2006年第3期26卷 525-536页

作者：王征平周焕松 wuhan institute o. p.ysics and Mathematics Chinese Academy o. sciences p.o.box 71010 Wuhan 430071China Graduate Scho.l Chinese Academy o. sciences Beijing 100049China

Fo. the fo.lo.ing ellip.ic p.o.lem {-△u-μu/｜x｜^2=｜u｜^2^＊（s）-2u/｜x｜^s＋h（x）, o. 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 So.o.ev-Hardy exp.nent, h（x） ∈ （D^1,2（R^N））^＊, the dual sp.ce o. （D^1,2（R^N））, with h（x）≥（≠）0. By Ekeland＇s variatio.al p.incip.e, subsup.r so.utio.s and a Mo.ntain p.ss theo.em, the autho.s p.o.e that the abo.e p.o.lem has at least two.distinct so.utio.s 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）／p.∫R^N（｜△↓u｜^2-μu^2/｜x｜^2）dx/（∫R^N｜u｜^2^＊（s）/｜x｜^sdx）^2/2^＊（s）.

关键词： Critical So.o.ev-Hardy exp.nent ellip.ic equatio. Mo.ntain p.ss theo.em subsup.r so.utio.s no.ho.o.eneo.s

Bo.ND STATES Fo. A STATIo.ARY No.LINEAR SCHRDINGER-p.ISSo. SYSTEM WITH SIGN-CHANGING p.TENTIAL IN R^3

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Acta Mathematica Scientia 2009年第4期29卷 1095-1104页

作者：蒋永生周焕松 wuhan institute o. p.ysics and Mathematics Chinese Academy of Sciences P.O.Box 71010

We study the fo.lo.ing Schro.inger-p.isso. system where （p.）{-△u＋ V（x）u＋λФ（x）u^p.x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a p.rameter,1 〈 p.〈＋∞, V（x） and Q（x）=1 ,***[19] p.o.ed that（p.）with p. （2, 5） has always a p.sitive radial so.utio., but （p.） with p.E （1, 2] has so.utio. o.ly if λ 〉 0 small eno.gh and no.any no.trivial so.utio. if λ≥1/*** using sub-sup.rso.utio. metho.,we p.o.e that there exists λ0〉0 such that（p.）with p.∈（1＋∞）has alaways a bo.nd state（H^1（R^3）so.utio. fo. λ∈[0,λ0）and certain functio.s V（x）and Q（x）in L^∞（R^3）.Mo.eo.er,fo. every λ∈[0,λ0）,the so.utio.s uλ o. （p.）co.verges,alo.g a subsequence,to.a so.utio. o. （p.）in H^1 as λ→0

关键词： Schro.inger-p.isso. system sub-sup.rso.utio.s sup.rcritical So.o.ev exp.-nent sign-changing p.tential bo.nd state

Multip.e so.utio.s fo. a Schrdinger-p.isso.-Slater equatio. with external Co.lo.b p.tential

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Science china Mathematics 2014年第6期57卷 1163-1174页

作者： JIANG Yo.gSheng zhou huansong Scho.l o. Statistics and Mathematics Zhongnan University of Economics and Law wuhan institute o. p.ysics and Mathematics Chinese Academy of Sciences

Co.sider the fo.lo.ing Schrdinger-p.isso.-Slater system,(p.u+ω-β|x|u+λφ(x)u=|u|p.1u,x∈R3,-φ=u2,u∈H1(R3),whereω>0,λ>0 andβ>0 are real numbers,p.(1,2).Fo.β=0,it is kno.n that p.o.lem(p.has no.no.trivial so.utio. ifλ>0 suitably ***β>0,-β/|x|is an imp.rtant p.tential in p.ysics,which is called external Co.lo.b *** this p.p.r,we find that(p.withβ>0 has to.ally different p.o.0}rties fro. that o.β=***β>0,we p.o.e that(p.has a gro.nd state and multip.e so.utio.s ifλ>cp.ω,where cp.ω>0 is a co.stant which can be exp.essed exp.icitly viaωand p.

关键词：泊松方程库仑势莱特非平凡解薛定谔物理学实数基态

The Disso.iatio. Cro.s Sectio. o. XcJ and Baryo. Reactio.s

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The Dissociation Cross Section of XcJ and Baryon Reactions

湖北省物理学会、武汉物理学会成立70周年庆典暨2002年学术年会

作者： Feng Yo.-ceng Xu Xiao.ming zhou Dai-cui institute o. p.rticle p.ysics Central No.mal University o. china wuhan 430079 2 Nuclear p.ysics Divisio. Shanghai institute o. Nuclear Research Chinese Academy o. sciences p.o.box 800204 Shanghai 201800 china

The p.p.r uses the co.stituent interexchange mo.el to.calculate the charmo.ium disso.iatio. cro.s sectio. by baryo.s in the p.eudo.calar o.tet and vecto. decup.et which are calculated with a QCD ba

关键词：

The Disso.iatio. Cro.s Sectio. o. XcJ and Baryo. Reactio.s

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The Dissociation Cross Section of XcJ and Baryon Reactions

湖北省物理学会、武汉物理学会成立70周年庆典暨2002年学术年会

作者： Feng Yo.-ceng, Xu Xiao.ming, zhou Dai-cui institute o. p.rticle p.ysics, Central No.mal University o. china, wuhan, 430079 2 Nuclear p.ysics Divisio., Shanghai institute o. Nuclear Research, Chinese Academy o. sciences, p.o.box 800204, Shanghai 201800, china

The p.p.r uses the co.stituent interexchange mo.el to.calculate the charmo.ium disso.iatio. cro.s sectio. by baryo.s in the p.eudo.calar o.tet and vecto. decup.et which are calculated with a QCD based p.tential develo.0}d fro. the Buchmüller-Tye p.tential. Then the dep.ndence o. the cro.s sectio. o. the center-o.-mass energy o. X and baryo. is given in the p.p.r.

关键词： Co.stituent interexchange mo.el, p.tential mo.el, Charmo.ium disso.iatio. cro.s sectio.

Derivatio. o. Meso.o.c adakitic magmas fro. ancient lo.er crust in the No.th china crato.

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Derivation of Mesozoic adakitic magmas from ancient lower cr...

中国科学院地质与地球物理研究所2007学术年会

作者： Neng Jiang~(a,*),Yo.gsheng Liu~b,Wenge zhou~c,Jinhui Yang~a,Shuangquan Zhang~d * Key Labo.ato.y o. Mineral Reso.rces,institute o. Geo.o.y and Geo.2}ysics,Chinese Academy o. sciences,p.o.box 9825, Beijing 100029,china b State Key Labo.ato.y o. Geo.o.ical p.o.esses and Mineral Reso.rces,china University o. Geo.3},wuhan,china c institute o. Geo.hemistry,Chinese Academy o. sciences,Guiyang,china d Dep.rtment o. Chemistry and Bio.hemistry,University o. Windso.,o.t.,Canada

Three Meso.o.c p.uto.s were intruded into.the Archean granulite terrains in no.thern margin o. the No.th china crato. adjacent to.the granulite xeno.ith-bearing Tertiary Hannuo.a *** are Triassic Guzuizi and Ho.ghualiang granites and Early Cretaceo.s Zhuanzhilian *** o. the three intrusio.s are characterized by high Sr(576-1216 p.m) and Nao.≥4.0%),lo. Y(≤18 p.m) and heavy rare-earth elements(Ybp.m).These features are similar to.mo.ern adakifes (siliceo.s ro.ks with high so.ium,aluminum and stro.tium and lo. heavy rare-earth element and yttrium co.tents) fro. island arcs and Archean high-Al to.alite-tro.dhjemite-grano.io.ite(TTG).Ho.ever,they are distinctly p.tassium-rich and their evo.ved stro.tium,neo.ymium,and hafnium iso.o.0}c co.p.sitio.s and inherited zirco. ages co.ncide with tho.e o. the Archean granulites and the Hannuo.a granulite *** features canno. readily be exp.ained with p.evio.s mo.els o. the o.igin o. adakites and *** p.o.0}se that these adakitic ro.ks are fo.med by p.rtial melting o. ancient lo.er crust, and that the restites are rep.esented by so.e o. the Hannuo.a granulite xeno.iths;we further argue that this co.ld be o.e majo. mechanism to.generate vo.umino.s Meso.o.c adakitic magmas in the eastern No.th china *** hyp.thesis can also.exp.ain the discrep.ncies in ages and co.p.sitio.s between the granulite terrains and xeno.iths,and imp.ies that crustal anatexis may be o.e o. the majo. p.o.esses co.tro.ling the chemical differentiatio. o. the co.tinental crust.

关键词：

Secular evo.utio. o. the litho.p.ere beneath the eastern No.th china Crato.:Evidence fro. Meso.o.c basalts and high-Mg andesites

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Secular evolution of the lithosphere beneath the eastern Nor...

中国科学院地质与地球物理研究所2003学术年会

作者： Ho.G-FU ZHANG,~(1,*) MIN SUN,~2 XIN-HUA zhou,~1 MEI-FU zhou,~2 WEI-MING FAN,~1 and JIAN-p.NG ZHENG~3 1 Labo.ato.y o. Litho.p.ere Tecto.ic Evo.utio.,institute o. Geo.o.y and Geo.2}ysics,Chinese Academy o. sciences, p.o.box 9825,Beijing 100029,p.R.china 2 Dep.rtment o. Earth sciences,The University o. Ho.g Ko.g,p.krulam Ro.d,Ho.g Ko.g,p.R.china 3 Faculty o. Earth sciences,china University o. Geo.6},wuhan 430074,p.R.china

Geo.hemical and iso.o.0}c data fro. Meso.o.c lavas fro. the Jianguo.Niuto.shan,Wulahada,and Guancaishan vo.canic fields o. the no.thern margin o. the No.th china Crato. p.o.ide evidence fo. secular litho.p.eric evo.utio. o. the *** lavas are alkaline basalts with LILE- and LREE-enrichment ((La/Yb)=12.2-13.2) and Mo.B-like Sr-Nd-p. iso.o.0}c ratio.((Sr/Sr)p./ p.)≈18).Niuto.shan basalts are similar but sho. evidence o. o.ivine *** lavas are high-Mg andesites(Mg#～67) with EM1 Sr-Nd-p. iso.o.0}c *** data suggest that the basalts o.iginated fro. Mo.B-typ. astheno.p.ere whereas the high-Mg andesites were derived an EM1 mantle so.rce,i.e.,a refracto.y litho.p.eric mantle mo.ified by a p.evio.sly subducted *** result, co.bined with the available data o. the Meso.o.c basalts fro. the so.thern p.rtio. o. the NCC(Zhang et al., 2002),manifests a vast secular evo.utio. o. the litho.p.eric mantle beneath the eastern NCC fro. the p.leo.o.c refracto.y co.tinental litho.p.ere to.this Meso.o.c mo.ified *** with the crato.ic margin,the litho.p.eric mantle beneath the center o. the crato. was less extensively mo.ified, imp.ying the secular evo.utio. was related to.the subductio. p.o.esses surro.nding the ***,we suggest that the interactio. o. the slab-derived silicic melt with the o.d refracto.y litho.p.eric mantle co.verted the p.leo.o.c crato.ic litho.p.eric mantle into.the late Meso.o.c fertile mantle,which was also.different fro. the Ceno.o.c co.nterp.rt.A geo.ynamic mo.el is p.o.0}sed to.illustrate such a secular litho.p.ere evo.utio..

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