含p-Laplace算子的Sturm-Liouville边值问题正解的性质

Properties of Positive Solutions to Sturm-Liouville Boundary Value Problems With p-Laplace Operators

研究了含p-Laplace算子的Sturm-Liouville边值问题正解的性质.利用p-Laplace算子的性质,使用L’Hpital(洛必达)法则和闭区间上连续函数的最值性定理,研究了含p-Laplace算子的Sturm-Liouville边值问题,得到了其正解存在的两个必要条件.最后给出了主要结论的应用.结论丰富了边值问题研究领域的内容,为利用计算机使用迭代技术求这类边值问题的近似解提供了新的渠道,推广了一些文献的结论.

The properties of positive solutions were investigated for a class of Sturm-Liouville boundary value problems with p-Laplace operators.Based on the properties of p-Laplace operators,and according to the L＇ Hopital＇s rule and the extreme value theorem for continuous functions on closed intervals,the Sturm-Liouville boundary value problems with p-Laplace operators were studied.The 2 necessary conditions for the existence of positive solutions were obtained.In the last part,the application of the main findings was given.The work enriches the content in the field of boundary value problems,and provides a new channel of using computer and iterative techniques to find approximate solutions to boundary value problems,meanwhile extending some conclusions in previous literatures.