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1、广义组合KDV方程孤立波的轨道稳定性摘要:应用Grillakis提出的轨道稳定性理论,研究了广义组合KDV方程ut+aupux+bu2pux+duxxx=0(a,b,d,p=C,p>0)的轨道稳定性.利用轨道稳定性理论和谱分析得到了一类特殊形式孤波解的稳定性.关键词:轨道稳定;孤立波;谱分析OrbitalstabilityofsolitarywavesofgeneralizedcompoundKDVequationsAbstract:TheabstractresultsofGrillakisareuseddirectlyandtheorbitalstability
2、ofsolitarywavesofcompoundKDV-typeequationwithnonlineartermsofanyorderisexamined.ut+aupux+bu2pux+duxxx=0(a,b,d,p=C,p>0).Theorbitalstabilityisobtainedbyusingtheabstractorbitalstabilitytheoryanddetailedspectralanalysis.Keywords:orbitalstability;solitarywaves;spectralanalysis一类二阶常微分方程组边值问
3、题三个正解的存在性李高尚,刘锡平,贾梅,李春岭,李芳菲(上海理工大学理学院,上海200093)摘要:利用Leggett-Williams不动点定理,研究了在Sturm-Liouville边界条件下的一类二阶常微分方程组多个正解的存在性,得到了至少三个正解存在的充分条件.关键词:边值问题;正解;不动点;锥ExistenceofthreepositivesolutionsinboundaryvalueproblemsofaclassofsecondorderordinarydifferentialsystemsLIGao-shang,LIUXi-ping,JIAMei
4、,LIChun-ling,LIFang-fei(CollegeofScience,UniversityofShanghaiforScienceandTechnology,Shanghai200093,China)Abstract:Boundaryvalueproblemsofaclassofsecondorderordinarydifferentialsystemsareconsidered.UnderSturm-Liouvilleconditions,theexistenceofatleastthreepositivesolutionsisprovedbyusi
5、ngLeggett-Williamsfixedpointtheorem.Keywords:boundaryvalueproblem;positivesolutions;fixedpoint;cone具有脉冲预防接种的SIQR流行病数学模型周艳丽1,王贺桥2,王美娟2,徐长永2(1.上海理工大学医疗器械学院,上海200093;2.上海理工大学理学院,上海200093)摘要:讨论了一类具有脉冲预防接种且传染率为双线性的SIQR传染病模型.在脉冲预防接种下,分析了无病周期解的存在性和全局渐近稳定性.关键词:预防接种;脉冲微分方程;基本再生数;周期解;全局渐近稳定性SIQ
6、RepidemicalmodelwithimpulsivevaccinationZHOUYan-li1,WANGHe-qiao2,WANGMei-juan2,XUChang-yong2(1.CollegeofMedicalInstrumentation,UniversityofShanghaiforScienceandTechnology,Shanghai200093,China;2.CollegeofScience,UniversityofShanghaiforScienceandTechnology,Shanghai200093,China)Abstract:
7、ASIQRmodelforspreadofinfectiousdiseaseinapopulationwithimpulsivevaccinationisdiscussed.Thereproductionnumberforthemodelisobtained,andtheexistenceandglobalstabilityofthedisease-freeperiodicsolutionareanalysed.Keywords:vaccination;impulsivedifferentialequations;basicreproductionnumber;p
8、eriod
