| R^N上一个p-Laplacian问题的无穷多个变号解（英文） |
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| 引用本文： | 洪明理.R^N上一个p-Laplacian问题的无穷多个变号解（英文）[J].上饶师范学院学报,2010,30(6):17-26. |
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| 作者姓名： | 洪明理 |
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| 作者单位： | 防灾科技学院,河北三河065201 |
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| 基金项目： | Acknowledgment The author would like to express her hearfful thanks to Prof. Li Yong- qing and Prof. Li Song - ying for their useful comments and suggestions. |
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| 摘 要： | 考虑下面这个p-Laplacian问题多重变号解的存在性：-△pu＋｜u｜（p-2）u=f（x,u）in RN,其中u∈W1,p（RN）（p≠2）.我们结合对称临界性原理,不变集的方法和极小极大的方法,在f（x,u）关于u是奇的和其它的假设条件下,获得了上述问题的一个无界的径向对称的变号解序列.在N=4或N=6时,通过选择一个非径向对称子空间使得它包含的所有非零函数都是变号的,运用对称山路引理和对称临界性原理,获得了上述问题的一个无界的非径向对称的变号解序列。
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| 关 键 词： | p-Laplacian 对称临界性原理 不变集的方法 多解 变号解 |
Infinitely Many Sign-changing Solutions for a p-Laplacian Equation in RN |
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| HONG Ming-li.Infinitely Many Sign-changing Solutions for a p-Laplacian Equation in RN[J].Journal of Shangrao Normal College,2010,30(6):17-26. |
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| Authors: | HONG Ming-li |
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| Institution: | HONG Ming-li(Institute of Disaster-Prevention Science and Technology,Sanhe,065201,China) |
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| Abstract: | In this paper, we study a p-Laplacian elliptic equation -△pu+|u|(p-2)u=f(x,u) in RN,u∈W1,p(RN)(P≠2). Applying Principle of Symmetric Criticality and the invariant set method, we obtain infinitely many radial sign-changing solutions for the above equation under some assumptions on f. Besides, using the symmetric Mountain Pass Theorem and Principle of Symmetric Criticality, we also obtain infinitely many nonradial sign-changing solutions for the above equation when N=4or N≥6. |
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| Keywords: | p-Laplacian principle of symmetric criticality invariant sets multiple solutions sign-changing solutions |
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