具有連續(xù)型時(shí)滯非線性微分方程振動(dòng)性的研究.pdf

1、黑龍江大學(xué)碩士學(xué)位論文具有連續(xù)型時(shí)滯非線性微分方程振動(dòng)性的研究姓名：張新申請學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：任洪善20080422黑龍江大學(xué)碩士學(xué)位論文AbstractThetheoryoffunctionaldifferentialequationsisanimportantbranchoftheresearchareaofdifferentialequations，whichiscalledFDEorDDEforshortTh

2、esystematicresearchesinthisfieldanditsapplicationsbeganattheendof1940’SSofartherearemanyvaluablemonographsThetheoryiswidelyusedinbiologyphysics，controltheoryandengineeringproblemsIntherecentyearsoscillationforfunctionald

3、ifferentialequationshasdrawnincreasingattentionAgreatnumberofresearchresultsinthisdirectionhavebeenabtainedInthispaper：westudyoscillationforthreedifferentkindsofdelaydifferentialequationsoftheform(1)nonlinearneutralhyper

4、bolicequationwithcontinuouslydistributedtimedelay外㈤丕(吣瑚馴t岫7“／(xt))]爰∽丕∽瑚至圳亂))J=a(t)Au(z，t)∑ak(t)Au(z，t—Pk(￡))一Cg(z：t：∈)，【u(z：g(t，∈))]咖(∈)，withboundarycondition(z：t)∈Q【0，oc)三G，皇蘭砉凳』皇p(z：t)t上(z：亡)=。(2)higherordernonlinearn

5、eutraldelaydifferentialequationz(￡)c(￡)z(￡一7)】‘n)／p(t：f)，(zb(￡，f)】)打(f)=o‘，o(3)secondordernonlinearneutraldelayeddifferentialequationp(￡)妒(z@))z7(￡)】7q(t)，(茁(t)：z(丁(￡)))夕(z7(亡))=0ByusingGreenformula：Riccatitransformation

6、，Janseninequality，methodofPhi—los’integralaverageandKiguradgzeLemma，wedealwiththeabovedifficultprob—lems，establishoscillationcriteriaforthemandgeneralizeexistingknownresultsKeywords：timedelay；hyperbolictype；neutraltype；R