嚴格凸性與變分形式的非線性橢圓特征值問題的多重解.pdf

1、華中師范大學碩士學位論文嚴格凸性與變分形式的非線性橢圓特征值問題的多重解姓名：許美娟申請學位級別：碩士專業(yè)：應用數學指導教師：李工寶20080501AbstractInthispaper，westudytheeXistenceofmultipleweaksolutio璐tothef0llawingnolllinearellipticeigem礎uepmblemofanequationindiVergenceform：竺翟‘z。u))=入

2、，(札)，inQ：onaQpA)whereQ∈冗Ⅳisaboundedopendomain，入∈R1andⅣ≥2，whilethenonlinearitiesn：Q冗Ⅳ_RⅣand廠：R1_R1satisfycertainstructuralconditionsEspecially廠isof∞一1)一s釓Wi扎eoratin矗nityusinganewThreecriticalPointsTheoremin【3】，、陽getthee)(

3、istenceofatleastthreesolutionsto(縱)forAinsomeopenintervalAcR1，underweakerassumptio璐onA(z，∈)，where塊A(z，蕁)=n(z，∈)Thekeypointisthatweonlyas8umethatA(z，字)0，suchthatfora11yz∈Q，∈，卵∈RⅣ，∞，字)丟∞，卅丟∞，曠棖刊pas【14】andotherrelatedworl【s