攝動對稱非線性橢圓方程的多解.pdf

1、福建師范大學(xué)碩士學(xué)位論文攝動對稱非線性橢圓方程的多解姓名：黃麗容申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李永青2001.4.1AbstractVariationalproblemswhichareinvariantundertheactionsofsymmetricgroupoftenpossessmultiplesolutions(egseef161andthereferencetherein)Butwhenthesymme—try

2、iSdestroyedbyaperturbationwhichiSnotsmalldoesthesameresultstillsurviveSuchkindofproblemshavebeenstudiedbymanyauthorsduringthelasttwodecadesandSOIlleinterestingresultsareaISOobtained(see171411Inthispaper，themultiplicityof

3、solutionstothefollowingellipticproblem。5n，(島)isconsidered，wherenC剛isasmoothboundeddomain，g∈c(a武)，g(x，t)isoddwithrespecttot，and，∈G(n風(fēng))Accordingtoz2～equivariantLjusternik—Schnirehnantheory[13】andthemethodinfll】，thispaperfo

4、llows，generalizesthepreviousresultsandobtainstheexistenceofsolutionsinthefollowingcases：(1)when，(z，“)三，(z)，equation一△“=Aa(x)ug(x，u)十，(。)or一△Ⅱ=aa(x)u9(z，u)，l，(z)hasinfinitelysolutions(intheweaksense)(2)Whilen(z)三0，(島)hasi

5、nfinitelysolutions(intheweaksense)Hereu∈wj∥issaidtobeaweaksolutionof(島)wemeanthatJj一△一vdx=A矗a(z)luLp2uvdx如9(z，u)vdz如f(z，u)vdzholdsforany“∈w：”In0，wegiveanintroductionofthispaper；In51，somepreliminariesandwell—knownnotionsa