Oscillatory behavior of nonlinear advanced differential equations with a non-monotone argument

Abstract

Consider the first-order nonlinear advanced differential equation
x′(t)-p(t)f(x(τ(t)))=0, t≥t₀,
where p(t) is are nonnegative function on R and τ(t) is non-monotone or nondecreasing function such that τ(t)≥t for t≥t₀. 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.