二階Hamilton系統(tǒng)和p-Laplace系統(tǒng)周期解的存在性.pdf

1、河海大學(xué)碩士學(xué)位論文二階Hamilton系統(tǒng)和pLaplace系統(tǒng)周期解的存在性姓名：劉小運(yùn)申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：安天慶20080301AbstractByusingthegeneralizedmountaintheoremofEHRabinowitzandthelinkingth∞r(nóng)emofMartinSchechterincriticalpointtheorywestudytheexistenceoftheper

2、iodicsolutionforsecondorderHamiltoniansystems絮鼉，二，‘三嬰刀Vcherer0，F(xiàn)(tx)∈C(nTI。RN置)isI羽)一《D=j(o)一瓤乃=0。。Tperiodicint；andconsidertheordinarypLaplaci缸systems一。一(‘)I：一(f!V豫曩f))Wherep1，To，(f，砷∈C，(【o，71。尺“，R)isI“o卜J(丁)=z’(o一一(D=0‘

3、。。TperiodicintusingthegeneralizedmountainthcoronandthesaddlepointtheoremofPHRabinowitzweprovethattheconditionsforscgondordcrHamilloniansystemarealsoinpositionforordinarypLaplaciansysternsundertheassumptionsofsuppandsub—P

4、potentialconditionThemaincontentofthispaperisdividedintotwochapters：Inchaptertwoandthreo，WOdiscussexistenceofsolutiontothesecondordel“Hamiltoniansystemsundertheconditions0∈0(o，乃，&lira呻趔盟等掣姐I工I‘州一。l工rInchapterfourandfivew

5、ediscussexistenceofsolutiontotheordinarypLaplaciansystemsunderthefollowingthreeconditions：(VF(t，x)vx)≤，∥(f，力，(VF(t，力，vx)一apF(t，力9oo，0，∥(f，工)s(VF(t，力，糾，Keywords：Hamiltoniansystems；ordinarypLaplaciansystems；erificalpoints；