Global Attractivity of the Zero Solution for Wright's Equation

Abstract. In a paper published in 1955, E.M. Wright proved that all solutions of the delay differential equation z(t) = −αz(t − 1)(1 + z(t)) converge to zero for α ∈ [0, 1.5], and conjectured that this is even true for α ∈ [0, π/2]. The present paper provides a computer-assisted proof that for α ∈ [1.5, 1.5705], this delay differential equation has no periodic solution with an amplitude larger than a particular, explicit number. This means a proof for more than 99.5% of what was conjectured by E.M. Wright.