非線性算子方程的變號(hào)解存在性多解性及其應(yīng)用.pdf

1、東北大學(xué)碩士學(xué)位論文非線性算子方程的變號(hào)解存在性多解性及其應(yīng)用姓名：孟鵬申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：孫濤20041201東北大學(xué)碩士學(xué)位論文ABSTRACTExistenceofSignChangingSolutionsandMultipleSolutionsforNonlinearOperatorEquationsandItsApplicationsABSTRACTTheconetheoryisanimportantme

2、thodofdiscussingtheexistenceofsolutionsfornonlinearoperatorequationsAtpresent，somevaluableresultshavebeenobtainedBut，Wecanfindthatmostofpreviousarticlesandpapersdiscussabouttheexistenceofpositivesolutionsandnonzerosoluti

3、onsfornonlinearoperatorequationsUptonowtheabstractresultsonsigh—changingsolutionsareseldomfoundFortheneedofsomepracticalproblems，seekingtheexistenceofsign—changingsolutionsofthembecomeshotspotnowInthispaper，theexistenceo

4、fsign—changingsolutionsandmultiplesolutionsfornonlinearoperatorequationsarediscussedbyusingtheconetheoryandthefixedpointtheoryinBanachspaceItisconcludedthatthetheoremofexistenceofsignchangingsolutionsfornonlinearoperator

5、equationsbyusinganuppersolutioninchapter3，consequently，acorollaryoftheexistenceofthree—solutionsfornonlinearoperatorequationsisinferredCombiningchapter3andpaper【4】，itisgiventhatthetheoremofexistenceoffour—solutionsfornon

6、linearoperatorequationsinchapter4，beside，thecharacterofsolutionispointedAtthesametime，theabstractresultsinthispaperareappliedtotwokindsofSturm—LiouvilletwopointboundaryvalueproblemsKeywordseigenvalue，fixedpointuniformlyp