具有S-L邊值條件正齊次p-Laplacian方程分類理論及非齊次方程解的存在性.pdf

1、南京師范大學碩士學位論文具有SL邊值條件正齊次pLaplacian方程分類理論及非齊次方程解的存在性姓名：仇應玉申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：董玉君20100507AbstractInthispaper，westudyindexclassificationtheoryofpLaplacianequation8withgeneralSturmLi。nvilleb。undaryvalueconditionsandsolvabil

2、ity。fn0小homogeneousequationsmchapter。ne，wegivepreliminarykn。wledgeandthemainresultsob。tainedinthispaperInchaptertw。，wefindac。mpletelycontinUOusoperat。r，theoriginal。p。eratorequationistransformedafixedpointproblemInchapter

3、t№e，wefirstgivetheclassificati。n。fthehom。geneous礦Laplacianequati。n(如(z，))，q(t)姊(z)=o，z(0)cospQ—z7(o)siIbQ=o，z(1)COSp∥一z，(1)sinpp：0，0≤Q警，孚盧≤7rpbydiscussingthetriVialandnon砸V1a1sol砸ons，andthenwediscussthesolvabilityfornonh

4、omogeneousequationInchapterfour，atfirst，weinvestigateclassificationtheoryofthePos卜tivehomogeneous礦Laplacianequation(％(z，))74g(t)％(z)一g一(o)如(z一)2o，z(o)cospo—z7(0)sinpa=0，。(1)co昂p—z7(1)sirbfl=0，0≤＆孚，等序7r口，themainmethodisPr

5、iifer7stransformation，andthenwediscussthenontrivialsolutionforassociatednonhomogeneousequationbymakinguse0tLeraySchauderdegreeKeywords：p—Laplacian；Sturm—LionviUeb。undaryvalueproblem；砌exclassificationtheory；Priifer7strans