| 吕定洋.非线性薛定谔-麦克斯韦方程无穷多高能解的存在性[J].井冈山大学自然版,2016,(6):6-10 |
| 非线性薛定谔-麦克斯韦方程无穷多高能解的存在性 |
| EXISTENCE OF INFINITELY MANY LARGE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-MAXWELL EQUATIONS |
| 投稿时间：2016-04-03 修订日期：2016-05-13 |
| DOI：10.3969/j.issn.1674-8085.2016.06.002 |
| 中文关键词: 薛定谔-麦克斯韦方程 变分方法 临界点理论 喷泉定理 高能解 |
| 英文关键词: Schrödinger-Maxwell equations variational methods critical point theory fountain theorem high energy solution |
| 基金项目:湖南省自然科学基金项目（14JJ7083）；湖南省教育厅科学研究项目（14C0253） |
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| 中文摘要: |
| 利用临界点理论研究了一类非线性Schrödinger-Maxwell方程，对位势V和非线性项f做适当假设，得到了方程无穷多高能解的存在性结果。本文允许V和f（x，t）t变号，即使在定号的情形下，所给出的条件仍比已有的结果弱，并且去掉了几乎所有文献中所做的lim(|t|→0)（f（x，t））/（t）=0的假设。与已有文献利用山路定理研究不同，本文利用喷泉定理，所得结果推广和改进了原有文献的结论。 |
| 英文摘要: |
| Based on the critical point theory, we study the existence of infinitely many high energy solutions for a class of nonlinear Schrödinger-Maxwell equations. Under certain assumptions on V and f, we obtain infinitely many large solutions for the equations. Furthermore, V and f (x,t) are allowed to be sign-changing. Even in definite case, our assumptions are weaker than the existing results. Different from mountain pass theorem in previous literatures, we conduct the study by using fountain theorem. Our experimental results improve and generalize the existing results. |
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