Oscillatory behavior for nonlinear homogeneous neutral difference equations of second order with coefficient changing sign

Abstract

In this article, we obtain sufficient conditions so that all solutions of the neutral difference equation $$ \Delta^{2}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k})=0, $$ and all unbounded solutions of the neutral difference equation $$ \Delta^{2}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k}) -u_nH(y_{\alpha(n)})=0 $$ are oscillatory, where \(\Delta y_n = y_{n+1}-y_n\), \(\Delta^2 y_n =\Delta(\Delta y_n)\). Different types of super linear and sub linear conditions are imposed on \(G\) to prevent the solution approaching zero or \(\pm \infty\). For more information see https://ejde.math.txstate.edu/Volumes/2020/87/abstr.html