A collection of examples of first order linear neutral differential delay equations having a nonoscillatory solution with lim sup = ∞ and lim inf = 0 at ∞ is given. This disproves a recent conjecture about the asymptotic behavior of solutions to such equations.

In a recent paper [1] I. B. Lazarevic announced an extension of results of L. Tornheim [2; Theorems 2 & 3] concerning points of contact between two distinct members of an n-parameter family and between a member of an n-parameter family and a corresponding convex function. In the proofs of these extensions [1; Theorems 3.1 & 3.2] use is made of Tornheim′s Convergence Theorem [2; Theorem 5]; however this theorem is not correctly applied in [1] since it requires distinct limiting nodes, and that hypothesis necessarily fails in the approach used in [1], In this note proofs of results more general than those in [1] are given independent of convergence theorems.

In this paper we consider the types of pairs of multiple zeros which a solution to the differential equation

can possess on an interval I of the real line. The results obtained generalize those in [2] and (for n = 3) in [3].

I. Let f satisfy the condition

1.1

for all t ∊ I, u0 ≠ 0, and all u 1, … u n-1.