| 具有Neumann边值的齐次p-Laplacian方程的指标分类理论 |
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| 引用本文： | 宋士民. 具有Neumann边值的齐次p-Laplacian方程的指标分类理论[J]. 宿州学院学报, 2009, 24(1) |
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| 作者姓名： | 宋士民 |
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| 作者单位： | 南京师范大学,数学与计算机科学学院,江苏,南京,210097 |
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| 摘 要： | 通过建立指标分类理论讨论了一维p-Laplacian方程(φp(u′))′+q(t)φp(u)=0,a.e on[0,1]在Neumann边值u′(0)=0=u′(1)条件下平凡解和非平凡解的存在性,其中φp(s)=s p-2s,p>1,q∈L∞(0,1)。
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| 关 键 词： | 齐次p-Laplacian方程 Neumann边值 Prüfer变换 指标分类理论 |
The Index Classification Theory for Neumann Boundary Value with Homogeneous p-Laplacian Equation |
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| SONG Shi-min. The Index Classification Theory for Neumann Boundary Value with Homogeneous p-Laplacian Equation[J]. Journal of Shuzhou College, 2009, 24(1) |
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| Authors: | SONG Shi-min |
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| Affiliation: | SONG Shi-min(Department of Mathematics; Nanjing Normal University; Jiangsu 210097; China); |
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| Abstract: | In this paper,we investigate the existence of trivial solutions and nontrivial solutions for homogeneous p-Laplacian equation(p(u′))′+q(t)p(u)=0,a.e on ,u′(0)=0=u′(1),wherep(s)=|s|p-2s,p>1,q∈L∞(0,1).Our methods are based on prüfer transformation and index classification theory. |
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| Keywords: | homogeneous p-Laplacian Neumann problem prüfer transformation index classification theory |
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