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 SCHR?DINGER-MAXWELL EQUATIONS

利用临界点理论研究了一类非线性Schr?dinger-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limf(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。

Based on the critical point theory, we study the existence of infinitely many high energy solutions for a class of nonlinear Schrodinger-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.