Second-order Reverse Order Delay Differential Equations And Anti-sequence Of ¦µ-laplacian Periodic Solution Optimal Conditions

In this paper, we show that the monotone iterative technique pro-duces two monotone sequences that converge uniformly to extremal so-lutions for the periodic second-order delay differential equation and pe-riodic delay 0- laplace equation. Moreover, we obtain optimal existence conditions with upper and lower solutions in the reverse order.We consider the following second-order delay differential equation: y"(t) = f(t,y(t),y(t-T),y'(t)), Vt R,where f(t, u, v, w} : R4 - R is a continuous function, and f(t+T, u, v, w) f(t,u,v,w), T>0, r>0.In this paper, we study the scalar T- periodic problem :where f(t, u, v) : R3 - R is a continuous function, and f(t + T, u, v) = f (t,u,v)), T>0.