一類超線性橢圓方程解的集中現(xiàn)象.pdf

1、華東師范大學(xué)博士學(xué)位論文一類超線性橢圓方程解的集中現(xiàn)象姓名：荊瑞華申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：FrankPacard周風(fēng)20050501AbstractInthisthesis，westudytheconcentrationphenomenaforsemilinearellipticproblemswithsnpereriticalnonlinearityInthefirstpartweconstructpositives

2、olutionsofthesemilinearellipticproblem△uA札Up=0withhomogeneousDirichletboundaryconditionsinaboundedsmoothdomainQcR“(N≥4)，whentheexponentPissupercriticalandcloseenoughto而N2andtheparameterA∈RissmallenoughAsP。萬(wàn)N巧2andA_0atsom

3、eappropriatedrate，thesesolutionshave”multiplebubbles”atfinitelymanyofpointswhicharethecriticalpointsofafunctionwhosedefinitioninvolvestheGreen’Sfunctionof—AwithhomogeneousDirichletboundaryconditionOurresultinthispartexte

4、ndstheresultofDelPinoDolbeaultandMussoin[DDMl】whennisaballandthesolutionsareradiallysymmetricInthesecondpart，weconstructpositivesolutionstothesanlesupercriticalequationforN=3，thatiswithP=54EWhentheparameterAisapositiveco

5、nstantinsomerangeand￡_0wealsoconstructasequenceofpositivesolutionswith”multiplebubbles”atafinitenumberofpointsFinally，weconsidertheproblem△u1u19—1“十Ei，(z)=0inaboundeddomainQcRⅣ(N≥3)，andu=sigontheboundaryofn，where￡0andP=等

6、鬟EHerethefunctions，∈Co，。(Q)andg∈C2。(off)forsomeo∈(0，1)，Wewillconcludethattheproblemadmits”multiplybubbles”solutionswithfinitesingularpointswhosepositionsarerelatedtotheGreen’Sfunctionandthefunctions，andgWegivesomeapplica