| 四阶超线性奇异微分方程正解存在的充分必要条件 |
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| 引用本文： | 赵增勤. 四阶超线性奇异微分方程正解存在的充分必要条件[J]. 数学学报, 2007, 50(6): 1425-143. DOI: CNKI:SUN:SXXB.0.2007-06-028 |
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| 作者姓名： | 赵增勤 |
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| 作者单位： | 曲阜师范大学数学科学学院 曲阜 |
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| 基金项目： | 国家自然科学基金(10471075)，山东省自然科学基金(Y2006A04)，高教博士点专项科研基金(20060446001) |
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| 摘 要： | 利用范数形式的锥拉伸与压缩不动点定理,对一类四阶奇异超线性微分方程边值问题做了研究,得到C~2[0,1]正解与C~3[0,1]正解存在的充分必要条件,也得到C~2[0,1]正解的不可比较性等解的性质.
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| 关 键 词： | 奇异边值问题 四阶超线性 正解 |
| 文章编号： | 0583-1431（2007）06-1425-10 |
| 收稿时间： | 2006-01-04 |
| 修稿时间： | 2006-01-04 |
A Necessary and Sufficient Condition for the Existence of Positive Solutions of Fourth Order Singular Superlinear Differential Equations |
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| Zeng Qin ZHAO. A Necessary and Sufficient Condition for the Existence of Positive Solutions of Fourth Order Singular Superlinear Differential Equations[J]. Acta Mathematica Sinica, 2007, 50(6): 1425-143. DOI: CNKI:SUN:SXXB.0.2007-06-028 |
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| Authors: | Zeng Qin ZHAO |
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| Affiliation: | College of Mathematics Sciences, Qufu Normal University, Qufu 273165, P. R. China |
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| Abstract: | This paper investigates a class of fourth order singular sublinear bound- ary value problems.A necessary and sufficient condition for the existence of C~2[0,1] positive solutions as well as C~3 [0,1] positive solutions is given by using fixed point the- orem of cone expansion of norm type.We also obtaied the incomparability of C~2 [0,1] positive solutions. |
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| Keywords: | singular boundary value problem fourth order superlinearity positive solution |
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