达举霞. 四阶两点边值问题3个对称正解的存在性[J]. 华南师范大学学报(自然科学版), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014
引用本文: 达举霞. 四阶两点边值问题3个对称正解的存在性[J]. 华南师范大学学报(自然科学版), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014
DA Juxia. The Existence of Three Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014
Citation: DA Juxia. The Existence of Three Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014

四阶两点边值问题3个对称正解的存在性

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

  • 摘要: 应用广义的Leggett-Williams不动点定理,研究了四阶两点边值问题 u^\left( 4 \right)\left( t \right)=f\left( u\left( t \right) \right)\ \ \ \ \ \left( t\in \left 0, 1 \right \right), u\left( 0 \right)=u\left( 1 \right)=0, u''\left( 0 \right)=u''\left( 1 \right)=0 正解的存在性, 其中f:\mathbbR\to \left 0, +\infty \right)连续. 在f满足适当的增长条件下, 得到该问题至少存在3个对称正解.

     

    Abstract: Applying the generalized Leggett-Williams fixed-point theorem, the existence of positive solutions to the fourth-order boundary value problem is studied: u^\left( 4 \right)\left( t \right)=f\left( u\left( t \right) \right)\ \ \ \ \ \left( t\in \left 0, 1 \right \right), u\left( 0 \right)=u\left( 1 \right)=0, u''\left( 0 \right)=u''\left( 1 \right)=0, where f:\mathbbR\to \left 0, +\infty \right) is continuous. Under some conditions on f, there exist at least three symmetric positive solutions.

     

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