17312.一類卷積型非線性積分方程的解的研究

1、一類卷積型非線性積分方程的解的研究專業(yè)名稱：應(yīng)用數(shù)學(xué)申請人：林玉鳳指導(dǎo)教師：黃榮里副教授論文答辯委員會主席：矗多連廣西師范大學(xué)碩士學(xué)位論文一類卷積型非線性積分方程的解的研墨一一———————————————————————————————————————————————————————————————————————————————一Thestudyofsolutionsforaclassofnonlinearintegralequat

2、ionsotconvolutiontypeAuthor：LinYnfengSupervisor：RongliHuangMajor：AppliedMathematicsSpeciality：DifferentialequationGrade：2012ABSTRACTTheresearchaboutthesolutionsofintegralequations，weoftenstudiedtheexistenceanduniquenesso

3、fthesolution，andabigpartstudiesalsofocusontheasymptoticbehaviorofthesolutionTheexistenceanduniquenessofthesolutiontotheequationisthebasictheoreminthetheoryofordinarydifferentialequationWhilestudyingtheasymptoticbehavioro

4、ftheuniquesolutionofthisequation，morepreciselyiSstudyingtheexistenceofmonotonesolutionsoftheequationInrecentyears，anumberofdomesticandforeignma土hema舾cianshavededicatedtesearchinthisareaIn2008OLipovanstudiedtheexistencean

5、duniquenessofsolutionsofaclassofnonlinearintegralequations，anddiscussedtheasyraptoticbehaviorofthesolutionin2014ThispaperextendstheresultsofOLipovan，bvusingthesimilarmethods，itisdiscussedthattheexistenceanduniquenessofth

6、esolutionabouttheequationaswellasitsasymptoticbehavior，whichareamoregeneralclassofconvolutionnonlinearintegralequationswhenP≥1，itobtainsthefollowingresults：Inthefirstpart，weshowthatthereexistsanuniquenonnegativesolutionf

7、ortheequationLetUSconsidertheintegralequation：threefunctionsareinvolvedintheequationincluding圣、L(t)andP(t)，where圣needstomeetthreeconditionsweset，andtheseconditionsensurethat西isstrictlyincreasing，withtheinverse圣1：[0，o。)4f

8、0，∞)；respectivelyL(t)andP(t)arecontinuouspositivefunctionsontheinterval【0，∞)，andP㈨isnotidenticallyzero，itiseasytoknowthatL(t)andP(t)arecontinuouslydifferentiable，letP≥1andu(t)istheunknownfunctionUndertheseassumptions，wes

9、tudytheexistenceanduniquenessofsolutionsofthepromotedequation，attheBathetime，weDro、佗thattheequationexistsanonnegativesolutionwhenP≥1byusingtheSchanderfixedpointtheoremandrelatedlemmaInthesecondpart，wemainlystudytheasympt

10、oticbehavioroftheuniquesolutionofthisequationForthispurpose，wegivethesameconditionsensuringthefunction垂andinverse圣一1aremonotonous；respectivelyL(t)andP(t)axecontinuouspositivefunctionsontheintervalf0，∞)，andP(t)isnotidenti

11、callyzero，aswellasu(t)istheunknownfl】nctioⅡUndertheseconditions，byuseoftherelatedknowledgeofmathematicalanal—vsisandapagoge，weprovethatifPisanon—decreasingfunctionandP≥1，theequationhasthefollowingasymptoticbehaviorofsolu