| 具超线性增长非线性项的拟线性椭圆型方程共振问题 |
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| 引用本文： | 黄晨,贾高,黄利娜.具超线性增长非线性项的拟线性椭圆型方程共振问题[J].上海理工大学学报,2016,38(3):205-210,262. |
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| 作者姓名： | 黄晨 贾高 黄利娜 |
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| 作者单位： | 上海理工大学理学院, 上海 200093;上海理工大学理学院, 上海 200093;上海理工大学理学院, 上海 200093 |
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| 基金项目： | 国家自然科学基金资助项目(11171220);沪江基金资助项目(B14005) |
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| 摘 要： | 在非线性项具有超线性增长条件下,研究了拟线性椭圆型方程的共振问题.通过建立拟线性算子与线性算子的一种关系,依据Shapiro在加权Sobolev空间中建立的紧嵌入定理和推广的Brouwer定理,运用截断方法证明了近似方程的解存在;借助Sobolev理论、Fatou引理和Lebesgue控制收敛定理证明了上述近似解一致有界;利用投影技巧和Galerkin方法得到共振问题的非平凡解的存在性.
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| 关 键 词： | 加权Sobolev空间 拟线性椭圆型方程 超线性增长 |
| 收稿时间： | 2015/5/17 0:00:00 |
Resonance Problem of a Quasilinear Elliptic Quation with Superlinear Nonlinearities |
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| HUANG Chen,JIA Gao and HUANG Lina.Resonance Problem of a Quasilinear Elliptic Quation with Superlinear Nonlinearities[J].Journal of University of Shanghai For Science and Technology,2016,38(3):205-210,262. |
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| Authors: | HUANG Chen JIA Gao and HUANG Lina |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | The resonance problem of a quasilinear elliptic equation with superlinear nonlinearities were focused.By establishing the relationship between the quasilinear operators and linear operators, according to the Shapiro-type compact embedding theorem and Brouwer''s theorem, the existence of solutions of the approximate equation was revealed.With the help of the Sobolev theory, Fatou''s Lemma and Lebesgue dominated convergence theorem, the uniform boundness of the approximate solutions was proved.By using the projection technique and the Galerkin method, the existence of nontrivial solutions of the resonance problem was revealed. |
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| Keywords: | weighted Sobolev space quasilinear elliptic equation superlinear growth |
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