简介:WeinvestigatethenonlinearSchrdingerequationiut+△u+|u|p-1u=0with1+4/N
2)(whenN=1,2,1+4/N
2>||Q||(1-sc)/sc|▽Q||2,theneitheru(t)blowsupinfiniteforwardtimeoru(t)existsgloballyforpositivetimeandthereexistsatimesequencetn→+∞suchthat||▽u(tn)||2→+∞.HereQisthegroundstatesolutionof—(1—sc)Q+△Q+|Q|p-1Q=0.Asimilarresultholdsfornegativetime.Thisextendtheresultofthe3DcubicSchr(o|¨)dingerequationobtainedbyHolmertothegeneralmass-supercriticalandenergy-subcriticalcase.
简介:Inthispaper,weareconcernedwiththesymmetricpositivesolutionsofa2n-orderboundaryvalueproblemsontimescales.Byusinginductionprinciple,thesymmetricformoftheGreen’sfunctionisestablished.Inordertoconstructanecessaryandsufficientconditionfortheexistenceresult,themethodofiterativetechniquewillbeused.Asanapplication,anexampleisgiventoillustrateourmainresult.
简介:Inthispaper,themodifiedextendedtanhmethodisusedtoconstructmoregeneralexactsolutionsofa(2+1)-dimensionalnonlinearSchr¨odingerequation.WiththeaidofMapleandMatlabsoftware,weobtainexactexplicitkinkwavesolutions,peakonwavesolutions,periodicwavesolutionsandtheir3Dimages.
简介:Inthispaper,weprovetheglobalexistenceoftheweaksolutiontotheviscousquantumNavier-Stokes-Landau-Lifshitz-Maxwellequationsintwo-dimensionforlargedata.ThemaintechniquesaretheFaedo-Galerkinapproximationandweakcompactnesstheory.
简介:Inthispaper,weinvestigatetheglobalexistenceandlongtimebehaviorofstrongsolutionsforcompressiblenematicliquidcrystalflowsinthreedimensionalwholespace.TheglobalexistenceofstrongsolutionsisobtainedbythestandardenergymethodundertheconditionthattheinitialdataareclosetotheconstantequilibriumstateinH~2-framework.IftheinitialdatasinL~1-normarefiniteadditionally,theoptimaltimedecayratesofstrongsolutionsareestablished.WiththehelpofFouriersplittingmethod,onealsoestablishesoptimaltimedecayratesforthehigherorderspatialderivativesofdirector.