Department of Mathematics, Faculty of Science, University of Žilina, 010 26 Žilina, Slovakia
Copyright © 2011 J. Diblík and M. Kúdelčíková. This is an open access article distributed under the
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Solutions of the equation are considered for . The existence of two classes of positive solutions which are asymptotically different is proved using the retract method combined with Razumikhin's technique. With the aid of two auxiliary linear equations, which are constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.