帶調(diào)和勢(shì)的隨機(jī)非線性Schrodinger.pdf

1、四川師范大學(xué)碩士學(xué)位論文帶調(diào)和勢(shì)的隨機(jī)非線性Schrodinger姓名：李姣申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：張健20090430OnaclassofStochasticNonlinearSchrSdingerEquationwithaHarmonicPotentialMajor：PureMathematicsPostgraduate：JiaoLiSupervisor：JianZhangAbstract：Inthispaper，

2、wedevotetoinvestigatingthefollowingstochasticnonlinearSchrSdingerequationwithaharmonicpotential，Jut一(Au—lzJ2釓b入J讓12。U)=∈Byusingstochasticanalysisandbasictheoriesofpartialdifferentialequations，andthenintermsofestimatingth

3、eexpectationofenergyfunctional，wederivethefollowingresults：1Fortherepulsiveandsubcriticalstochasticequation，wederivetheglobalexistenceofitssolutions；2Forthecriticalandsupercriticalstochasticequation，weprovethatanygivenin

4、itialdatawithsufficientnegativeenergydevelopstoasingularityinfinitetimewithapositiveprobility；3Forthecriticalandattractivestochasticequationintwodimensionspace，wederiveglobalexistenceofitssolutionswithsufficientlysmallin