变系数三阶周期边值问题的正解

作者：姚庆六 Qing-liu变系数三阶周期边值问题正解variablecoefficientboundaryvalueproblemssolutionsfixedpointtheoremonconehammersteinboundaryvalueproblemvariablepositivesolutionstransformationnonlinearterm非线性项不动点定理existence积分方程存在性making转换

摘要：研究了变系数非线性三阶用期边值问题的正解,非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-serski不动点定理获得了1～2个正解的存在性. Abstract： The positive solutions of a nonlinear third-order periodic boundary value problem with variable coefficient are studied.The nonlinear term may be singular with respect to the space variable.By making use of suitable transformation,the problem is transformed into a Hammerstein integral equation.By applying Guo-Krasnosel'skii fixed point theorem on cone,the existence of one and two po sitive solutions is proved.

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