OSCILLATORY BEHAVIOROF NONLINEAR ADVANCED DIFFERENTIAL EQUATIONS WITH A NON-MONOTONE ARGUMENT

Abstract

Consider the first-order nonlinear advanced differential equation x'9t) - p(t)f(x)tau(t))) = 0, t >= t(0), where p (t) is nonnegative function on R and tau(t) is non-monotone or nondecreasing function such that tau(t) >= t for t >= t(0). Under these assumptions we researched oscillatory behaviour of solutions of nonlinear advanced differential equations and we obtain new oscillation criteria, involving limsup and liminf. An example illustruting the result is also given.