在Neumann边界条件下Schrdinger方程的多解和变号解  

Multiple and sign-changing solutions for Schrdinger equation with Neumann boundary condition

作　　者：金云娟[1] 

机构地区：[1]丽水学院数学系,浙江丽水323000

出　　处：《安徽大学学报（自然科学版）》2009年第1期9-12,共4页Journal of Anhui University(Natural Science Edition)

摘　　要：在非线性项为渐近线性条件下,研究一类非线性Schrdinger方程的Neumann边值问题,先证明这个方程至少有一个正解和一个负解,再说明极小正解与极大负解存在且均是局部极小值点,最后利用改进的山路引理和下降流不变集得到除了正负解外还有两个变号解的结论.In this paper,we studied a nonlinear Schrodinger equation with Neumann boundary condition when the nonlinearity was under the asymptotically linear conditions. Firstly, we proved the equation had a positive solution and a negative solution at least, and then to showed the existence of very small positive solution and extremely negative solution, moreover, they were local minimum points. Finally, by using of the improved mountain pass lemmas and invariant sets of descending flow, we got two sign-changing solutions except positive and negative solutions.

关 键 词：NEUMANN边界条件 下降流不变集 变号解 

分 类 号：O175[理学—数学]