【摘要】 利用变分方法与临界点理论,特别是临界群与Morse理论,结合矩阵理论与空间维数,同时考虑正、负能量泛函的临界点,研究了一维非线性离散椭圆共振问题解的多重性.在一定的假设条件下,得到了此类问题至少存在两个非零解的两类新的充分条件,并给出了具体应用的实例.结果表明:在相同的假设条件下,一维共振问题比多维共振问题得到的解更多.更多还原

【Abstract】 By using the variational method and critical point theory,especially critical group and Morse theory,combined with the matrix theory and space dimension,taking into account the critical points of both positive and negative energy functional,the multiplicity of solutions of 1-dimensional nonlinear discrete elliptic resonant problem was investigated.Under some assumptions,two kinds of new sufficient conditions were obtained under which there exist at least two nonzero solutions.An example was given to verify the obtained results.The results showed that,under the same assumptions,the number of known solutions of 1-dimensional resonant problem is more than that of multidimensional resonant problem.更多还原