简介:Inthispaper,byusingtheGuo-Krasnoselskii'sfixed-pointtheorem,weestablishtheexistenceandmultiplicityofpositivesolutionsforafourth-ordernonlineareigenvalueproblem.Thecorrespondingexamplesarealsoincludedtodemonstratetheresultsweobtained.
简介:Inthispaper,weconsiderthefollowingproblem{-Δu(x)+u(x)=λ(u~p(x)+h(x)),x∈R~N,u(x)∈h~1(R~N),u(x)>0,x∈R~N,(*)whereλ>0isaparameter,p=(N+2)/(N—2).Wewillprovethatthereexistsapositiveconstant0λ*,auniquesolutionforλ=λ*.Furthermore,(*)possessesatleasttwopositivesolutionswhenλ∈(0,λ*)and3≤N≤5.ForN≥6,undersomemonotonicityconditionsofhweshowthatthereexistsaconstant0
简介:Byapplyingiterativetechnique,weobtaintheexistenceofpositivesolutionsforasingularRiemann-Stieltjesintegralboundaryvalueprobleminthecasethatf(t,u)isnon-increasingrespecttou.
简介:Carbonclothmodifiedbyhydrothermaltreatmentinammoniawaterisdevelopedasthepositiveelectrodewithhighelectrochemicalperformanceforvanadiumredoxflowbatteries.TheSEMshowsthatthetreatmenthasnoobviousinfluenceonthemorphologyofcarboncloth.XPSmeasurementsindicatethatthenitrogenousfunctionalgroupscanbeintroducedonthesurfaceofcarbonclothsuccessfully.TheelectrochemicalperformanceofV(IV)/V(V)redoxcoupleonthepreparedelectrodeisevaluatedwithcyclicvoltammetryandlinearsweepvoltammetrymeasurements.TheN-dopedcarbonclothexhibitsoutstandingelectrochemicalactivityandreversibilitytowardV(IV)/V(V)redoxcouple.TherateconstantofV(IV)/V(V)redoxreactiononcarbonclothcanincreaseto2.27×10-4cm/sfrom1.47×10-4cm/safternitrogendoping.ThecellusingN-dopedcarbonclothaspositiveelectrodehaslargerdischargecapacityandhigherenergyefficiencycomparedwiththecellusingpristinecarboncloth.TheaverageenergyefficiencyofthecellusingN-dopedcarbonclothfor50cyclesat30mA/cm2is87.8%,4.3%largerthanthatofthecellusingpristinecarboncloth.ItindicatesthattheN-dopedcarbonclothhasapromiseapplicationprospectinvanadiumredoxflowbatteries.
简介:在这份报纸,在证明二存在的作者目的形式$$\left的部分微分边界价值问题结果({{P_{一,b}}}\right)\left\{{_{u\left(0\right)=u\left(1\right)=0,{D^{\alpha-3}}u\left(0\right)=一,u'\left(1\right)=-b}^{{D^\alpha}u\left(x\right)+f\left({x,u\left(x\right)}\right)=0,x\in\left({0,1}\right)}}\right.$$3<4,D是标准Riemann-Liouville部分衍生物并且一,b是nonnegative常数。首先,作者建议那f(x,t)=p(x)t,与(1,1)并且是的pnonnegative可能在x=单个的连续功能0或x=1并且满足与Karamata常规变化理论有关的一些条件。一些潜在的功能和Sch上的联合锋利的估计?uder修理了点定理,作者证明问题的一个唯一的积极连续答案的存在(P0,0)。如此的一个答案上的全球估计也被获得。为了说第二存在,结果,作者假定那一,b是nonnegative常数以便+b>0并且f(x,t)=t(x,t),与(x,t)nonnegative是连续的工作在(0,吗1)牵慦散猠摥浩湥獴映潲?慈桩?楒敶?慂楳?敷敲椠癮獥楴慧整??洠瑥潨?慢敳?湯攠晦'太B爠湡敧?剅?慷?獵摥琠?獡敳獳攠潣祳瑳浥爠獩?景倠??琨敨琠瑯污漠??倠??敳獮瑩癩汥?湡?捡畣慲顰?顰??
简介:Inthispaper,weareconcernedwiththesymmetricpositivesolutionsofa2n-orderboundaryvalueproblemsontimescales.Byusinginductionprinciple,thesymmetricformoftheGreen’sfunctionisestablished.Inordertoconstructanecessaryandsufficientconditionfortheexistenceresult,themethodofiterativetechniquewillbeused.Asanapplication,anexampleisgiventoillustrateourmainresult.