| 带P-Laplacian算子的四点四阶奇异边值问题的对称正解 |
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| 引用本文： | 栾世霞,赵艳玲.带P-Laplacian算子的四点四阶奇异边值问题的对称正解[J].应用数学学报,2011,34(5). |
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| 作者姓名： | 栾世霞 赵艳玲 |
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| 作者单位： | 1. 曲阜师范大学数学科学学院,曲阜,273165
2. 定陶县职业教育中心,定陶,274100 |
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| 基金项目： | 山东省自然科学基金(ZR2009AL016)资助项目 |
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| 摘 要： | 本文主要利用上下解方法和Schauder不动点定理,在更广泛的条件下研究了一类带PLaplacian算子的四点四阶奇异边值问题的对称正解的存在性.克服了对非线性微分算子φp(u″)]″Fredholm抉择定理和极大值原理不能使用的困难,改进并推广了最近的一些已知结果.
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| 关 键 词： | P-Laplacian算子 奇异边值问题 上下解 对称正解 Schauder不动点定理 |
Symmetric Positive Solutions of Fourth-order Four-point Boundary Value Problems with P-Laplacian Operator |
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| LUAN SHIXIA
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ZHAO YANLING.Symmetric Positive Solutions of Fourth-order Four-point Boundary Value Problems with P-Laplacian Operator[J].Acta Mathematicae Applicatae Sinica,2011,34(5). |
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| Authors: | LUAN SHIXIA ZHAO YANLING |
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| Institution: | LUAN SHIXIA (School of Mathematical Sciences,Qufu Normal University,Qufu 273165) ZHAO YANLING (Dingtao County Vocational Education Center,Dingtao 274100) |
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| Abstract: | This paper is concerned with the fourth-order singular BPVs.Under a general assumption,the existence of symmetric positive solution are obtained by the method of upper-lower solutions and Schauder's fixed point theorem.Predholm alternative theorem and minimax theorems are invalid here and our results generalize many recent studies. |
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| Keywords: | P-Laplacian operator singular boundary value problem lower and upper solutions symmetric positive solution Schauder's fixed point theorem |
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