We consider a second order nonlinear difference equation ?2 yn = anyn+1 + f(n, yn, yn+1) , n ∈ N . (E) The necessary conditions under which there exists a solution of equation (E) which can be written in the form yn+1 = αnun + βnvn , are given. Here u and v are two linearly independent solutions of equation ?2 yn = an+1yn+1 , ( lim n→∞ αn = α < ∞ and lim n→∞ βn = β < ∞) . A special case of equation (E) is also considered.
展开▼
机译：我们考虑一个二阶非线性差分方程？2 yn = anyn + 1 + f（n，yn，yn + 1），n∈N。 （E）给出了可以以yn + 1 =αnun+βnvn形式表示的方程式（E）的解的必要条件。在这里，u和v是方程式？2 yn = an + 1yn + 1的两个线性独立解，（lim n→∞αn=α<∞和lim n→∞βn=β<∞）。还考虑了方程（E）的一种特殊情况。
展开▼
