Triple Positive Solutions to Initial-boundary Value Problems of Nonlinear Delay Differential Equations

In this paper, we consider the existence of triple positive solutions to the boundary value problem of nonlinear delay differential equation [GRAPHICS] where phi : R -> R is an increasing homeomorphism and positive homomorphism with phi(0) = 0, and x(t) is a function in C([-tau,0],R) defined by x(t)(sigma) = x(t + sigma) for -tau <= sigma <= 0. By using a fixed-point theorem in a cone introduced by Avery and Peterson, we provide sufficient conditions for the existence of triple positive solutions to the above boundary value problem. An example is also presented to demonstrate our result. The conclusions in this paper essentially extend and improve the known results.