李宪, 达举霞, 章欢. 四阶两点边值问题n个对称正解的存在性[J]. 华南师范大学学报(自然科学版), 2024, 56(1): 123-127. doi: 10.6054/j.jscnun.2024015
引用本文: 李宪, 达举霞, 章欢. 四阶两点边值问题n个对称正解的存在性[J]. 华南师范大学学报(自然科学版), 2024, 56(1): 123-127. doi: 10.6054/j.jscnun.2024015
LI Xian, DA Juxia, ZHANG Huan. The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 123-127. doi: 10.6054/j.jscnun.2024015
Citation: LI Xian, DA Juxia, ZHANG Huan. The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 123-127. doi: 10.6054/j.jscnun.2024015

四阶两点边值问题n个对称正解的存在性

The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem

  • 摘要: 应用单调迭代法,研究了四阶两点边值问题 \begingatheredu^(4)(t)=f(u(t)) \quad(t ? 0, 1), \\u(0)=u(1)=0, u^\prime \prime(0)=u^\prime \prime(1)=0\endgathered 正解的存在性。在边值问题满足特定的条件下, 证明了该问题存在n个对称正解。

     

    Abstract: Applying of the monotone iterative technique, the existence of positive solutions to the fourth-order boundary value problem is studied: \begingatheredu^(4)(t)=f(u(t)) \quad(t ? 0, 1), \\u(0)=u(1)=0, u^\prime \prime(0)=u^\prime \prime(1)=0.\endgathered The above boundary value problem has n symmetric positive solutions under certain conditions.

     

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