具非標準增長條件的四階橢圓方程弱解存在性與多解性.pdf

1、蘭州大學碩士學位論文具非標準增長條件的四階橢圓方程弱解存在性與多解性姓名：臧愛彬申請學位級別：碩士專業(yè)：數(shù)學基礎(chǔ)數(shù)學指導(dǎo)教師：范先令20080501蘭州大學2008屆碩士學位論文AbstractInthispapertheauthorfirstlyshowstheinterpolationinequalitiesforderivativcsinvariableexponentLeSseeSobolevspacesbyapplyingth

2、emaximalfunctionoperatorandSobolevintegralrepresentation，Asapplications，theauthorprovesacompactSobolevembeddingtheoremandanewLandau—KomogorovtypeinequalityforthesecondorderderivativeanddiscussestheequivalentnolTnSinthesp

3、acew名’p(。’(Q)nW2p(z)(Q)Onthebaseoftheseconclusions，theauthorbythecriticalpointtheorydiscussestheexistenceandmultiplicityoftheweaksolutionsforthefollowingellipticequationsoffourthorderwithnonlinearitieshavethenonstandardg

4、rowthconditionsofAmbrosetti—Rabinowitztyperespectively：J△轟z)u=f(x，仳)z∈Q，Iu=△亂=0z∈Oft；andJ△轟z)札=f(x，Ⅱ)z∈Q，Iu=V讓=0z∈Off；where鋒(z)釓：=A(1／Xulp(z)一2△u)Atthesametime，theexistenceandmultiplicityoftheweaksolutionsfortheequations

5、asabovewithoutAmbrosetti—RabinowitztypegrowthCOnditionalediscussedtooKeyWords：VariableexponentSobolevspaces；Maximalfunctionoperator；Fourthorderellipticequations；Ceramicondition；LandauKolmogorovtypeinequality；p(z)一Biharmo