一類混合型非線性二階橢圓型方程組解的存在性與唯一性.pdf

1、一‰必⑧天畢大薯碩士學位論文學科專業(yè)：應用數(shù)學作者姓名：邱凌云指導教師：姚妙新教授T濰一_望‘rTr已々“盯士2006年1月ABSTRACTInthispaper，thesecondordernonlinearellipticsystem二竺三羔囂二三影二hh2黑，∽【一△口=，2(z)礦一啦@)護(z)礦P()，一witha1，p21and071isconsideredinQ，whichisaboundedopensubsetofRN

2、N≥3Underasetofsuitablehypothesesonfunction五，m，kandP，itisshownthatthissystempossessesapositivesolution(u，t，)∈(儼，9(Q)n伊(固)2ThepaperismainlydividedintofoursectionsInthefiertsection，wegiveanintroductionofthispaperItincludest

3、hebackgroundofthisproblem，themainworkinthispaperandsomeopenproblemsNext，weprovidesomebasaldefinitionsandtheoriesinthesecondsection，suchasthemaximumprinciple，HSldercontinuitySchaudertheoryand∞on，whicharefoundationofthelat

4、erworkThethirdsectionofthispapersolvestheexistenceanduniquenessofthepositiveentresolutionstoacertainsecondordernonlinearellipticequationTosolvethisproblem，upperandlowermethodandcomparisonlemmaareintroducedAtlast，weestabl

5、ishthemaintheoremofthispaper，theexistenceanduniquene船ofpositivesolutionsforsystem()KeyWords：nonlinearellipticequation；positivesolution；upperlowermethod；multimonotonicoperator；reactiondiffusionequation；equilibriumsolution