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中文摘要：
文章考虑了一类离散非线性薛定谔方程，利用临界点理论结合Nehari流形方法，证明了该方程的驻波解的存在性．特别地，当非线性项是奇函数时，得到了多解的结果．同时提高了经典的Ambrosetti—Rabinowitz超线性条件．
英文摘要：
We consider a class of discrete nonlinear Schrodinger equations. By using critical point theory in combination with the Nehari manifold approach,we prove the existence of standing wave solutions for the equations. Especially, we obtain infinitely many solutions of the equations when the nonlinearity is odd. The classical Ambrosetti-Rabinowitz superlinear condition is improved.
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