Oscillations of difference equations with several oscillating coefficients (Q1724010)

Summary: We study the oscillatory behavior of the solutions of the difference equation \(\Delta x(n)+\sum^m_{i=1}p_i(n)x(\tau_i(n))=0\), \(n\in\mathbb N_0\) [\(\nabla x(n)-\sum^m_{i=1}p_i(n)x(\sigma_i(n))=0\), \(n\in\mathbb N\)] where \((p_i(n)), 1\leq i\leq m\) are real sequences with oscillating terms, \(\tau_i(n)\) [\(\sigma_i(n)\)], \(1\leq i\leq m\) are general retarded (advanced) arguments, and \(\Delta\) [\(\nabla\)] denotes the forward (backward) difference operator \(\Delta x(n)=x(n+1)-x(n)\) [\(\nabla x(n)=x(n)-x(n-1)\)]. Examples illustrating the results are also given.