| 一类周期非线性差分方程的基态解 |
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| 引用本文： | 买阿丽,孙国伟. 一类周期非线性差分方程的基态解[J]. 数学杂志, 2016, 36(6): 1173-1182 |
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| 作者姓名： | 买阿丽 孙国伟 |
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| 作者单位： | 运城学院应用数学系, 山西 运城 044000,运城学院应用数学系, 山西 运城 044000 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11526183; 11371313; 11401121); the Natural Science Foundation of Shanxi Province (2015021015) and Foundation of Yuncheng University (YQ-2014011; XK-2014035). |
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| 摘 要： | 本文研究了一类二阶周期非线性差分方程基态解的存在性问题.利用临界点理论结合Nehari流形方法,获得了此类方程基态解的存在性.在比经典AR条件更一般的超二次条件下,本文结论推广了已有的结果,并举例说明此类方程解的存在性.
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| 关 键 词： | 非线性差分方程 Nehari流形 基态解 临界点理论 |
| 收稿时间： | 2015-06-25 |
| 修稿时间： | 2016-01-04 |
GROUND STATE SOLUTIONS FOR NONLINEAR DIFIERENCE EQUATIONS WITH PERIODIC COEFFICIENTS |
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| MAI A-li and SUN Guo-wei. GROUND STATE SOLUTIONS FOR NONLINEAR DIFIERENCE EQUATIONS WITH PERIODIC COEFFICIENTS[J]. Journal of Mathematics, 2016, 36(6): 1173-1182 |
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| Authors: | MAI A-li and SUN Guo-wei |
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| Affiliation: | Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China and Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China |
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| Abstract: | In this paper, we study the existence of ground state solutions for nonlinear second order diffierence equations with periodic coefficients. Using the critical point theory in combination with the Nehari manifold approach, the existence of ground state solutions is established. Under a more general super-quadratic condition than the classical Ambrosetti-Rabinowitz condition, the results considerably generalize some existing ones. Finally, an example is also presented to demonstrate our results. |
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| Keywords: | nonlinear diffierence equations Nehari manifold ground state solutions critical point theory |
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