Large time behavior of a linear delay differential equation with asymptotically small coefficient
1 Department of Mathematics, University of Pannonia, P.O. Box 158, Veszprém, H-8201, Hungary
2 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, H-6720, Hungary
Boundary Value Problems 2014, 2014:114 doi:10.1186/1687-2770-2014-114
Dedicated to Professor Ivan KiguradzePublished: 14 May 2014
The linear delay differential equation , , is considered, where and the coefficient is continuous and small in the sense that , . It is shown that the large time behavior of the solutions can be described in terms of a special solution of the associated formal adjoint equation and the initial data. In the special case of the Dickman-de Bruijn equation, , , our result yields an explicit asymptotic representation of the solutions as .
MSC: 34K06, 34K25, 11A51.