On oscillation, convergence and boundedness of solutions of some nonlinear difference equations with multiple delay
In the first part of the paper the authors consider the equation \[ x_{n+1}=\lambda_nx_n+\sum_{i=1}^r\alpha_i(n)F(x_{n-m_i}). \] Various sufficient conditions are established which guarantee oscillation of equation, resp. existence of nonoscillatory solution, resp. the situation where solutions either oscillate or have certain asymptotic behavior. In the second part of the paper, the equation of the form \[ x_{n+1}=G(x_n,x_{n-1},\dots,x_{n-m}) \] is studied. Sufficient conditions are established guaranteeing convergence of every solution to zero (resp. to the positive equilibrium), resp. persistence of every solution.
scientific article; zbMATH DE number 5554979