时间尺度上一类半正三阶三点边值问题的解的存在性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 455-465.

时间尺度上一类半正三阶三点边值问题的解的存在性

桑彦彬^1,2|韦忠礼²

1.中北大学数学系太原 030051|2.山东大学数学学院济南 250100

收稿日期:2009-12-04 修回日期:2011-01-10 出版日期:2011-04-25 发布日期:2011-04-25
基金资助:
山西省青年科技基金(2009021001-2)、国家自然科学基金(10901145, 10971046)、山西省高等学校优秀青年学术带头人支持计划和山东省自然科学基金(ZR2009AM004)资助

Existence of Solutions to a Semipositone Third-order Three-point BVP on Time Scales

SANG Yan-Bin^1,2, WEI Zhong-Li²

1.Department of Mathematics, North University of China, Taiyuan 030051|2.School of Mathematics, Shandong University, Jinan 250100

Received:2009-12-04 Revised:2011-01-10 Online:2011-04-25 Published:2011-04-25
Supported by:
山西省青年科技基金(2009021001-2)、国家自然科学基金(10901145, 10971046)、山西省高等学校优秀青年学术带头人支持计划和山东省自然科学基金(ZR2009AM004)资助

摘要/Abstract

摘要：

该文通过构造涉及非线性项的辅助函数与考察此辅助函数在有界集上的性质, 获得了一类时间尺度上半正三阶三点边值问题的解的存在性, 此处的非线性项下方有界. 采用的主要工具为锥拉伸与锥压缩型的Krasnosel'skii不动点定理.

关键词: 半正, 时间尺度, 三阶, 三点, 多解性

Abstract:

In this paper, by constructing an auxiliary function concerned with nonlinear term and considering the properties of this auxiliary function on bounded sets, the existence of solutions is established for a semipositone third-order three-point BVP on time scales, where the nonlinear term is lower bounded. The main tool is based on Krasnosel'skii fixed point theorem of cone expansion-compression type.

Key words: Semipositone, Time scales, Third-order, Three-point, Multiplicity

中图分类号:

34B10

桑彦彬, 韦忠礼. 时间尺度上一类半正三阶三点边值问题的解的存在性[J]. 数学物理学报, 2011, 31(2): 455-465.

SANG Yan-Bin, WEI Zhong-Li. Existence of Solutions to a Semipositone Third-order Three-point BVP on Time Scales[J]. Acta mathematica scientia,Series A, 2011, 31(2): 455-465.

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