1、湖南大學(xué)碩士學(xué)位論文具有變號(hào)擾動(dòng)的PLaplace方程的正解及多重解存在性問(wèn)題姓名：彭麗輝申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：戴求億20040312AbstractLetQC艫beasmoothboundarydomain，f(x)∈廠=C。(豆)＼o)，0P1，AOq∈(o，P一1)U(p—l，o。)，△，Ⅱ=div(IVulp一2Vu)isSOcalledpLaplaceoperatorThemainpurposeofthis

2、paperistoidentifynecessaryandsufficientconditionsonnaridf(x)whichensuretheexisteace，ormultiplicitiesofnonnegativesolutionsfortheproblem()。Thestrategytoovercomecorrespondingdifficultiesistoconstructthenonnegativesubsoluti

3、onofproblem(11)andanalyzetheasymptoticbehaviorofthesolution札^ofproblem(11)asA0orA_o。Infact，throughthoseanalyse，wefoundthattheexistenceofnonnegativesolutionofproblem(11)iscloselyrelatedtothesolvabilityofthefollowingproble

4、m：f一△p妒=，(T)，z∈Q，妒≥0，z∈n，I妒=0，z∈Of2，alselatedtothefollowinghomogeneousproblem：瞄№卜。1譏簍KeyWords：InhomogeneousP—LaplaceEquation；DirichletProblemVariationMethod；MountainPassLemma；NonnegativeSolution；Sup—subSolutionMethod；PSC