一类非线性薛定谔方程组无穷多解的存在性

摘要

讨论了一类非线性薛定谔方程组无穷多解的存在性。在假设的V (x)， b (x)， f (x)条件下，通过减弱喷泉定理的条件，运用变形的喷泉定理，证明了相关方程组的无穷多解的存在性。较扰动方法更加简捷。%In this paper, the existence of infinitely many solutions for the nonlinear schr¨odinger system is discussed. Under the certain assumptions on V (x), b (x), f (x) the existence of the infinitely many solutions for the correlation equations is proved by weakening the fountain theorem conditions and using the variant fountain theorem. It is simpler than the perturbation method.