超二次条件下差分方程的周期解

Periodic Solutions for Difference Equations under Superquadratic Condition

研究了二阶差分方程△(p(t)△u(t-1))+W(t,u(t))=0周期解的存在性,其中W(t,u)=-K(t,u)+F(t,u)。假设K满足"夹逼"条件和F在原点与无穷远处是超二次的,分别用环绕定理和山路引理得到了多重或无穷多周期解,推广了某些已知的结果。

This paper analyzes the existence of periodic solutions for the second order difference equations -△（p （t） △u （t - 1 ） ）＋△↓ W （t, u （t） ） = 0, where W （t, u ） =- K （t, u ） ＋ F （t, u ）. Assuming that K sat isfies t he ＂pinching＂ condition and is superquadratic at zero and at infinity,multiple periodic solutions and infinitely many solu- tions are obtained respectively with the linking theorem and Mountain Pass lemma. The results provide a gener- alization for some known ones.