雷策宇, 韩晓玲. 带变号格林函数的三阶三点边值问题的正解的存在性[J]. 华南师范大学学报(自然科学版), 2021, 53(2): 104-109. doi: 10.6054/j.jscnun.2021032
引用本文: 雷策宇, 韩晓玲. 带变号格林函数的三阶三点边值问题的正解的存在性[J]. 华南师范大学学报(自然科学版), 2021, 53(2): 104-109. doi: 10.6054/j.jscnun.2021032
LEI Ceyu, HAN Xiaoling. The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(2): 104-109. doi: 10.6054/j.jscnun.2021032
Citation: LEI Ceyu, HAN Xiaoling. The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(2): 104-109. doi: 10.6054/j.jscnun.2021032

带变号格林函数的三阶三点边值问题的正解的存在性

The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function

  • 摘要: 应用格林函数的性质和迭代法, 研究了一类具有变号格林函数的三阶三点边值问题 \left\ \beginarray*20c \beginarrayl u'''\left( t \right) = f\left( t,u\left( t \right) \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( t \in \left 0,1 \right \right),\\ u\left( 1 \right) = 0,u'\left( 0 \right) = u''\left( 0 \right),\alpha u''\left( \eta \right) + \beta u\left( 0 \right) = 0 \endarray \endarray \right. 正解的存在性, 其中, fC(0, 1×0, ∞), 0, ∞)), α∈0, 1, \frac27α < β < \frac23α, η\frac23, 1). 得到了该边值问题正解存在性的条件.

     

    Abstract: Using the properties of Green's function and the iterative method, the existence of positive solutions to a class of third-order three-point boundary value problems with sign-changing Green's function is studied: \left\ \beginarray*20c \beginarrayl u'''\left( t \right) = f\left( t,u\left( t \right) \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( t \in \left 0,1 \right \right),\\ u\left( 1 \right) = 0,u'\left( 0 \right) = u''\left( 0 \right),\alpha u''\left( \eta \right) + \beta u\left( 0 \right) = 0, \endarray \endarray \right. where fC(0, 1×0, ∞), 0, ∞)), α∈0, 1, \frac27α < β < \frac23α, η\frac23, 1). The conditions for the existence of positive solutions to the boundary value problem are obtained.

     

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