Special Session 99: Asymptotic expansion for nonoscillatory solutions of differential and difference equations
Contents
This talk is concerned with the oscillatory behavior of difference equations corresponding to the second-order nonlinear differential equation \(x'' + f(x)/t^2 = 0\), where \(f\) is continuous on \(\mathbb{R}\) and satisfies \(x f(x) > 0\) if \(x \neq 0\). Obtained results are represented as a pair of oscillation theorem and non-oscillation theorem. These results are best possible in a certain sense. A discrete version of the Riemann-Weber generalization of the Euler differential equation and its extended equations play an important role to prove our results. The proofs of our results are based on Riccati technique and phase plane analysis of a system.