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In this paper some sufficient conditions are obtained to insure the existence of positive solutions which is relatively bounded from one side for nonlinear neutral differential equations of second order.Weused the Krasnoselskii’s fixed point theorem and Lebesgue’s dominated convergence theorem to obtain new sufficient conditions for the existence of a Nonoscillatoryone side relatively boundedsolutions.These conditions are more applicable than some known results in the references. Three examples included to illustrate the results obtained.

EXISTENCE OF NONOSCILLATORY RELATIVELY BOUNDED SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS