摘要
<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)≡∞.
出版日期
2002年01月11日(中国期刊网平台首次上网日期,不代表论文的发表时间)