变号(k,n-k)共轭边值问题解的存在问题

苏华, 刘立山

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 261-270.

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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 261-270. DOI: 10.12386/A2015sxxb0026
论文

变号(k,n-k)共轭边值问题解的存在问题

    苏华1, 刘立山2
作者信息 +

The Solutions for Semipositone (k,n-k) Conjugate Boundary Value Problems

    Hua SU1, Li Shan LIU2
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文章历史 +

摘要

讨论了下列变号(k,n-k)共轭边值问题(SCBVP)正解的存在问题

其中n≥2, 1<k<n-1.对于0<t<1,非线性项f允许变号, 即本文允许非线性项f取负值并且可以无下界.本文利用不动点指数定理,在无任何单调性假设条件下,得到了边值问题正解的存在性结论.

Abstract

We consider the existence of positive solutions to the following semiposi-tone (k,n-k) conjugate boundary value problems (SCBVP): 

where n≥2, 1<k<n-1. The nonlinear function f may change sign for 0 < t < 1, i.e., we allow that the nonlinear term f is both semipositone and lower unbounded. Without making any monotone-type assumption, by using the fixed-point index theory, the existence of positive solution and many positive solutions are obtained.

关键词

变号共轭边值问题 / 下方无界 / 正解 / 不动点指数定理

Key words

semipositone conjugate boundary value problems / positive solutions / lower unbounded / fixed-point index theory

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苏华, 刘立山. 变号(k,n-k)共轭边值问题解的存在问题. 数学学报, 2015, 58(2): 261-270 https://doi.org/10.12386/A2015sxxb0026
Hua SU, Li Shan LIU. The Solutions for Semipositone (k,n-k) Conjugate Boundary Value Problems. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 261-270 https://doi.org/10.12386/A2015sxxb0026

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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)和山东省高校科研创新团队项目资助项目

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