| 一类半正二阶常微分方程边值问题正解的存在性 |
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| 引用本文： | 魏晋滢,王素云,李永军.一类半正二阶常微分方程边值问题正解的存在性[J].山东大学学报(理学版),2019,54(10):7-12. |
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| 作者姓名： | 魏晋滢 王素云 李永军 |
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| 作者单位： | 兰州城市学院数学学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目(11761044,11661048);兰州城市学院博士科研启动基金资助项目(LZCU-BS2015-01);兰州城市学院重点建设学科资助项目(LZCU-ZDJSXK-201706) |
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| 摘 要： | 考虑非线性二阶常微分方程边值问题u″+c(t)u+λf(t,u)=0, 00, c(·)∈C［0,1］满足-∞π2对t∈［0,1］成立, f:［0,1］×R+→R连续且满足f≥-L, L>0是常数。通过利用相应线性边值问题的Green函数及其性质和Krasnoselskii不动点定理,获得了问题正解的存在性结果。
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| 关 键 词： | 半正问题 边值问题 Green函数 正解 不动点定理 |
Existence of positive solutions to a semipositone second-order boundary value problem |
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| WEI Jin-ying,WANG Su-yun,LI Yong-jun.Existence of positive solutions to a semipositone second-order boundary value problem[J].Journal of Shandong University,2019,54(10):7-12. |
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| Authors: | WEI Jin-ying WANG Su-yun LI Yong-jun |
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| Institution: | School of Mathematics, Lanzhou City University, Lanzhou 730070, Gansu, China |
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| Abstract: | We consider the existence of positive solutions to the boundary value problemu″(t)+c(t)u+λf(t,u)=0, 0λ>0, c(·)∈C［0,1］ satisfies -∞π2 for t∈［0,1］, f:［0,1］×R+→R is continuous function and satisfies f≥-L, L>0 is a constant. By investigating the sign property of the Green function of the associated linear boundary value problem, we show the existence of positive solutions of semipositone problems. The proof of the main result is based on Krasnoselskii fixed point theorems in cone. |
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| Keywords: | semipositone problem boundary value problem Green function positive solution fixed point theorem |
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