The notion of quasi-asymptotic behavior for the space of Boehmians is introduced and studied. AMS Mathematics Subject Classification (2010): 44A40, 46F05, 41A60, 44A15, 46F12.

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...