具變號位勢的二階離散Hamilton系統(tǒng)的周期解和同宿軌.pdf

1、湖南大學(xué)博士學(xué)位論文具變號位勢的二階離散Hamilton系統(tǒng)的周期解和同宿軌姓名：鄧小青申請學(xué)位級別：博士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：庾建設(shè)20070907具變號位勢的二階離散Hamilton系統(tǒng)的周期解和同宿軌Abstract711heexistenceofsubharmouicsolutionsperiodicsolutionsandhomochnicorbitsofsecondordernonlineardiscreteHamilto

2、uiansystemswithpotentialchanginginsignisstudiedbyusingcriticalpointtheoryinthisdissertationAseriesofnewresultsareobtainedbychangingtheexistenceofsubharmonicsolutions，periodicsolutionsandhomocimicorbitsintotheexistenceofc

3、riticalpointsofthecorrespondingfunctionalonsuitablefunctionspaceThisdissertationiscomposedoffourchapters’I№contentsofthedissertationareintroduced嬲follows：Inchapter1，thehistoricalbackgroundandtherecentdevelopmentoftheprob

4、lemstobestudiedareintroduced，atthesametime，themaincontentsofthedissertationareoutlinedTheexistenceofsubharmonicsolutionsofakindofsecondordernonlineardiscreteHamiltoniansystemsisdiscussedinchapter2bynsi：ugLinkingTheoremIn

5、thesesystemsthepotentialcomprisestwofactors，oneisanonzeroperiodicfunctionwithzeromean，andtheotherisafunctionwhichsatisfiescertaingrowthconditionsSomesufficientconditionswhichcanguaranteethatthesesystemshaveatleastonenont

6、riviaisubharmouicsolutionareobtainedTheexistenceofperiodicsolutionsofaclassofsecondordernonlineardiscreteHamlltoniansystemswithsignchangingpotentialisconsideredinchapter3Inthesesystemsthepotentialnotonlyhasaperiodicfunct

7、ionwithnonzeromeanandchangingsign，butalsohasasymmetricmatrixvaluedperiodicfunctionthatisindefiniteinsignInsomeliteraturetheexistenceofperiodicsolutionsofaspecialcaseofthesesystemswithasymptoticallyquadraticpotentialiscon

8、sideredbyusingMorsetheorybutinthisdissertationthesesystemswithoutasymptoticallyquadraticpotentialarestudiedbyusingminimaxtheorem，andSOmesufficientconditionsoftheexistenceofatleastoneortwonontrivialperiodicsolutionsofthes

9、esystemsareobtainedTheresultsobtainedenrichanddevelopthetheoryofdiscreteHamiltoniansystemsTheexistenceofhomoclinicorbitsofakindofsecondorderselfadjointnonlineardiscreteHamiltoniansystemswithpotentialchanginginsignisstudi