| 关于一类带次临界指标的拟线性薛定谔方程的正解 |
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| 引用本文： | 汪继秀.关于一类带次临界指标的拟线性薛定谔方程的正解[J].湖北大学学报(自然科学版),2014(3):199-202,205. |
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| 作者姓名： | 汪继秀 |
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| 作者单位： | 湖北文理学院数学与计算机学院,湖北襄阳441053 |
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| 基金项目： | 湖北省教育厅科研计划项目（Qg0122504）资助 |
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| 摘 要： | 主要考虑一类拟线性薛定谔方程的正解,由于该方程所对应泛函不能定义在常用空间H1(RN)上,而且H1(RN)→嵌入Lq(RN)(2
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| 关 键 词： | 拟线性薛定谔方程 次临界指标 山路引理 正解 |
The positive solutions for subcritical quasilinear Schr6dinger equations |
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| WANG Jixiu.The positive solutions for subcritical quasilinear Schr6dinger equations[J].Journal of Hubei University(Natural Science Edition),2014(3):199-202,205. |
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| Authors: | WANG Jixiu |
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| Institution: | WANG Jixiu (School of Mathematics and Computer Science, Huhei University of Arts and Science, Xiangyang 441053,China) |
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| Abstract: | We considered the generalized quasilinear Schr6dinger equations, and so the functional for the equations didn＇t he defined in the space H1 （R^N）. To overcome this difficuhy, we made a variable replacement, the new function was well defined in H1 （RN）, in addition, the embedding H1（R^N）→Lq（R^N） （2〈Q〈2＊） was not compact, fortunately, Strauss proved that the embedding HI（R^N）→Lq （RN） （2〈Q〈2＊） was compact, where H1 （RN） was the radial space of U1 （RN）, therefore, we obtained the positive solutions for the studied equations by mountain pass lemma and maximum principle. |
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| Keywords: | quasilinear Schr6dinger equations subcritical exponents mountain pass 1emma positive solutions |
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