一类周期非线性差分方程的基态解

摘要

本文研究了一类二阶周期非线性差分方程基态解的存在性问题。利用临界点理论结合Nehari流形方法，获得了此类方程基态解的存在性。在比经典AR条件更一般的超二次条件下，本文结论推广了已有的结果，并举例说明此类方程解的存在性。%In this paper, we study the existence of ground state solutions for nonlinear second order difference equations with periodic coefficients. Using the critical point theory in combination with the Nehari manifold approach, the existence of ground state solutions is established. Under a more general super-quadratic condition than the classical Ambrosetti-Rabinowitz condition, the results considerably generalize some existing ones. Finally, an example is also presented to demon-strate our results.