一类带有强制位势的 Klein Gordon Maxwell 系统无穷多解的存在性

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。

The Existence of Infinitely Many Solutions for a Class of Klein-Gordon Maxwell System Involving the Coercive Potential

Cross-border tourism is one of tourism products with influence and development potential, and the exploitation and development of cross-border tourism can boost the tourism development and economic growth of border regions. Through the study of different types of cross-border tourism route(CBTR) in Europe and Africa, such as hiking, bicycle and safari, this paper finds that CBTR needs to construct stable and reliable mutual funds security mechanism, to form united and coordinated management operation mechanism, to have efficient and convenient free pass visa system, and to emphasize harmonious paragenesis tourist experience with green and environment protection. Based on international experience, China should use openness and cooperation to boost the breakthrough of border tourism, actively promote CBTR exploitation and construction, use mechanism innovation to build high quality CBTR, build effective and mutual investment, coordinative management, convenient border-pass system and operation mechanism, use green and safe tourism to realize CBTR sustainable development and really protect ecological environment and tourists safety.