简介:Theaimofthispaperistogiveasimpleproofoftherestrictiontheoremforthemaximaloperatorsonthed-dimensionalEuclideanspaceRd,whosetheoremwasprovedbyCarro-Rodriguezin2012.Moreover,weshallgivesomeremarksoftherestrictiontheoremforthelinearandthemultilinearoperatorsbyCarro-RodriguezandRodriguez,too.
简介:TheexistenceandorbitalinstabilityofstandingwavesforthegeneralizedthreedimensionalnonlocalnonlinearSchr¨odingerequationsisstudied.Bydefiningsomesuitablefunctionalsandaconstrainedvariationalproblem,wefirstestablishtheexistenceofstandingwaves,whichrelysontheinnerstructureoftheequationsunderconsiderationtoovercomethedrawbackthatnonlocaltermsviolatethespace-scaleinvariance.Wethenshowtheorbitalinstabilityofstandingwaves.Theargumentsdependupontheconservationlawsofthemassandoftheenergy.
简介:根据Cauchy—Schwarz不等式,得到了C^2(a,b])空间中函数的二阶导数的若干新积分不等式.