The Existence Of Positive Solutions Of A Class Of Even Order Nonlinear Differential Equations

In this paper, we study the existence of eventually positive solutions of even order nonlineardifferential equations of the form:(?)whereαandβare positive constants, n∈N+ and q(t):[T,∞)â†'(T,∞) is a continuous func-tion. We establish the necessary and suffcient conditions for the existence of eventually positivesolutions under the condition that 0 <β<α.