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二阶Sturm-Liouville特征值问题解的存在与非存在性 被引量：1

The Existence and Nonexistence of Positive Solutions for Second-Order Sturm-Liouville Eigenvalue Problems
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摘要 讨论了二阶Sturm-Liouville特征值边值问题解的存在性与非存在性,得到了边值问题至少有一个正解的特征值λ的存在区间的结论.进一步,给出了边值问题没有正解的特征值存在区间. We consider the existence and nonexistence of positive solutions for secondorder eigenvalue Sturm-Liouville boundary value problem.We shall show there is an interval such that for every λ in this interval,the existence of at least one positive solution to the boundary value problem is guaranteed,moreover there is no solution when λ is appropriate value.
作者 苏华 刘立山
机构地区 山东财经大学数学与数量经济学院 曲阜师范大学数学科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2014年第6期1241-1248,共8页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(11371221) 高等学校博士学科点专项科研基金(20123705110001) 山东省高等学校科研计划项目(J13LI12) 山东省高校科研创新团队项目资助项目
关键词 二阶奇异微分方程 上下解方法 正解 second-order singular differential equation lower and upper solutions positive solutions
分类号 O175.8 [理学—基础数学]
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参考文献11

  • 1韦忠礼.非共振多参数脉冲奇异边值问题的多解性[J].数学物理学报（A辑）,2006,26(3):431-439. 被引量：4
  • 2王俊禹,高文杰,张中新.Sturm-Liouville边值问题解的非存在性、存在性和多重性结果[J].数学学报（中文版）,2005,48(4):739-746. 被引量：7
  • 3Qi Zhang,Fuyi Li,Xiaoli Zhu.Multiple sign-changing solutions to the Sturm–Liouville boundary value problem with resonance[J].Applied Mathematics and Computation.2012(3)
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二级参考文献12

  • 1WEI ZHONGLI.EXISTENCE OF SOLUTIONS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS FOR NONLINEAR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS IN BANACH SPACES[J].Applied Mathematics(A Journal of Chinese Universities),1998,13(2):141-149. 被引量：3
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数学学报（中文版）
2014年 第6期

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