時滯雙曲方程、二階阻尼微分方程的振動性準則.pdf

1、黑龍江大學碩士學位論文時滯雙曲方程、二階阻尼微分方程的振動性準則姓名：李愛霞申請學位級別：碩士專業(yè)：應用數學指導教師：任洪善20080510黑龍江大學碩士學位論文AbstractOscillationtheoryoffunctionaldifferentialequationisanimportantbranchoftheresearchfieldoffunctionaldifferentialequations，whichhasdee

2、pbackgroundsofapplicationsItarisesinmanyresearchareas，suchasbiology，ecology，physiologyphysicsandSOonIntherecentyears，thestudyofoscillationforfunctionaldifferentialequationsattractswideattentionandgainsrichachievementsins

3、cientificresearchMostoftheresults，however，isdevotedtoequationswithdiscretedelays，whiletherearefewresultsforoneswithcontinuousdistributeddelaysandsecondordernonlineardamperdifferentialequationsInthispaper，weestablishoscil

4、lationcriteriafortheseequations，whichgeneralizeorimprovesomeexistingoscillationtheorems(see[1]一[101)ThepresentpaperisdividedintofoursectionsInchapter1，weintroducethebackgroundandpresentsituationofoscillationoffunctionald

5、ifferentialequationsInchapter2，weintroducemethodsofHfuction，averagethchniqueandtrasformationofRiccatitostudyoscillationresultsofahyperbolicdifferentialequationwithdelay象缸咖(xtrt惻DAup‰咖一知^跏k夕他㈣№㈣Inchapter3westudytheoscilla

6、tionforhigherordernonlinearpartialfunctiondifferentialequationofneutraltype殺M州愀M州叫】=妻“洲郇以))_／6如^剛㈨砌∽釧磁∽bythewayofturninghigherorderequationsintosecondorderoneswithH—methodW爸obtainsomeoscillationcriteriaInchapter4，westudy

7、oscillationresultsforasecondordernonlineardampeddifferentialequation(r(￡)妒(z’(￡)))’p(t)g(x7(亡))g(亡)‘廠(z(t))=0byusingaveragetechniqueKeywords：hyperbolicfuctionalequation；continuousdistributeddelay；dampeddifferentialequati