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

This paper studies the existence of eventually positive solutions and establishes the necessary and sufficent conditions for the existence of eventually positive solutions under the condition that 0<α<βfor the following even order nonlinear differential equations. (|u(n)(t)|α-1u(n)(t))(n)+q(t)|u(t)|β-1u(t)=0 whereαandβare positive constants, q(t):[0,∞)→(0,∞) is a continuous function.