简介：<正>WeareconcernedwiththefollowingDirichletproblem:-△u（x）=f（x,u）,x∈Ω.u∈H01（Ω）.（P）wheref（x,t）∈C（Ω×R）,f（x,t）/tisnondecreasingint∈RandtendstoanL∝-functionq（x）uniformlyinx∈Ωast→+∝（i.e.,f（x,t）isasymptoticallylinearintatinfinity）.Inthiscase.anAmbrosetti-Rabinowitz-typecondition,thatis.forsomeθ>2.M>0,0<θF（x.s）≤f（x,s）s,forall|s|≥Mandx∈Ω,（AR）isnolongertrue,whereF（x,s）=integralfromn=0tosf（x,t）dt.Asiswellknown,（AR）isanimportanttechnicalconditioninapplyingMountainPassTheorem.Inthispaper,withoutassuming（AR）weprove,byusingavariantversionofMountainPassTheorem,thatproblem（P）hasapositivesolutionundersuitable,conditionsonf（x,t）andq（x）.Ourmethodsalsoworkforthecasewheref（x,f）issuperlinearintatinfinity.i.e.,q（x）≡∞.

简介：Ekeland’svariationalprincipleisafundamentaltheoreminnonconvesanalysis.Itsgeneralstatementisasthefollowing:Ekeland’sVariationalPrinciple'’a:.LetVbeacompletemetricspace,andF:F—*-RU{+°°}alowersemicontinuousfunction,notidentically+00andboundedfrom,below.Lets>0begiven,andapointu^VsuchthatF(u)