| 一类两点边值问题正解的个数 |
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| 引用本文： | 程红梅,闫宝强. 一类两点边值问题正解的个数[J]. 应用泛函分析学报, 2012, 0(2): 213-218 |
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| 作者姓名： | 程红梅 闫宝强 |
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| 作者单位： | 山东师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金(10871120) |
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| 摘 要： | 讨论边值问题（（一v＇（r））~n）＇=λ（v~α＋v~β）,v＇（0）=v（1）=0,其中λ〉0是正参数.对（n-α）（n-β）〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~＊〉0,使得当0〈λ〈λ~＊时,此边值问题恰好存在两个正解;当λ=λ~＊时,此边值问题存在唯一一个正解;当λ〉λ~＊时,此边值问题不存在正解.
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| 关 键 词： | 边值问题 正解 存在性 |
Exact Number of Positive Solutions for A Class of Two-Point Boundary Value Problem |
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| CHENG Hongmei,YAN Baoqiang. Exact Number of Positive Solutions for A Class of Two-Point Boundary Value Problem[J]. Acta Analysis Functionalis Applicata, 2012, 0(2): 213-218 |
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| Authors: | CHENG Hongmei YAN Baoqiang |
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| Affiliation: | Department of Mathematics,Shandong Normal University,Ji’nan 250014,China |
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| Abstract: | In this paper,we consider the existence of positive solutions for the two-point boundaryvalue problems((-v’(r))~n)’ =λ(v~α+ v~β) and v’(0) =v(1) = 0,whereλ> 0 is a positive parameter.We show that the two-point boundary value problem has a unique positive solution forλ>0 when(n-α)(n-β)>0;and it has exactly two positive solutions for 0<λ<λ~*,exactly one forλ=λ~*,and none forλ>λ~* when 0 <α
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| Keywords: | boundary value problems positive solutions existence |
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