| 摘要: |
| 在非线性项满足局部（AR）条件下，研究并证实了带有强制位势的 Klein Gordon Maxwell系统无穷多解的存在性;证明的困难来源于该系统特有的项φ为隐函数,不能用u表示出来,利用引理和分析的一些技巧,克服了这一困难;最后基于变分原理,证明了带有强制位势的该系统具有山路几何结构和满足（PS）条件;再结合对称山路引理，获得了该系统无穷多解的存在性结果。 |
| 关键词: 系统 变分法 对称山路引理 无穷多解 |
| DOI： |
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| The Existence of Infinitely Many Solutions for a Class of Klein-Gordon Maxwell System Involving the Coercive Potential |
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YUAN Dong-lei, HE Shu-wen, WEN Xiao-bo1,2
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1.School of Mathematics and Statistics, Southwest University, Chongqing 400715,China;2.School of Science and Technology,Sichuan Minzu College, Sichuan Kangding 626001, China
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| Abstract: |
| The existence of infinite solutions of Klein Gordon Maxwell system with coercive potential is studied and proved under local (AR) condition. The unique term φ of the system is implicit function, which can’t be expressed by u. Some techniques of lemmas and analysis are used to overcome this difficulty. Based on variational principle, the existence of infinite solutions of Klein Gordon Maxwell system with coercive potential is proved. The system with compulsory potential has the geometric structure of mountain path and satisfies (PS) condition. Combining with the symmetric mountain path lemma, the results of the existence of infinite solutions of the system are obtained. |
| Key words: Klein Gordon Maxwell system variational method symmetric mountain pass lemma infinitely many solutions. |
