| 带变号系数的半线性边值问题的非负解（英） |
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| 引用本文： | 程建纲.带变号系数的半线性边值问题的非负解（英）[J].烟台大学学报(自然科学与工程版),2002,15(2):97-103. |
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| 作者姓名： | 程建纲 |
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| 作者单位： | 烟台大学,数学与信息科学系,山东,烟台,264005 |
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| 基金项目： | 国家自然科学基金资助项目 (10 0 710 6 6 )~~ |
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| 摘 要： | 利用Schauder不动点定理和上下解方法 ,对边值问题 1p(t) (p(t) y′(t) ) +a(t) f(t,y(t) ) =0 ,limt→ 0 +p(t) y′(t) =0 =y(1)讨论非负解的存在性 .其中 p∈C1(0 ,1)且在 (0 ,1)上 p>0 ,f≥ 0 ,对固定的 y函数 f(t,y)关于t是单调递减的 ,对固定的t函数f(t,y)关于 y是单调递增的 ,a∈C(0 ,1) 可以改变其符号 .
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| 关 键 词： | 变号系数 半线性边值问题 非负解 存在性 不动点定理 上下解方法 |
Nonnegative Solutions of Semilinear Boundary Value Problems with Coefficient that Changes Sign |
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| CHENG Jian,gang.Nonnegative Solutions of Semilinear Boundary Value Problems with Coefficient that Changes Sign[J].Journal of Yantai University(Natural Science and Engineering edirion),2002,15(2):97-103. |
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| Authors: | CHENG Jian gang |
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| Abstract: | This paper deals with the existence of nonnegative solutions to boundary value problems (1)/(p(t))(p(t)y′(t))′+a(t)f(t,y(t))=0,limt→0+ p(t)y′(t)=0=y(1) where p∈C1 (0,1) with p>0 on (0,1),f≥0,f(t,y) is nonincreasing with respect to t for each fixed y and nondecreasing with respect to y for each fixed t,and a∈C(0,1) may change sign. Our approach is based on the Schauder fixed point theorem. |
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| Keywords: | boundary value problem nonnegative solution existence fixed point theorem |
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