The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian

This paper deals with the multiplicity results of positive solutions of one-dimensional singular p-Laplace equation(φp(U´ (t)))´+ a(t)f(t, u(t), U´(t)) = 0, 0 t 1subject to the nonlinear boundary conditions αφp(u(0)) − βφp(U´(ξ)) = 0, γφp(u(1)) + δφp(U´(η)) = 0, where φp(x) = |x|^p−2x, p 1. By using the Avery-Peterson fixed point theorem, sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are obtained.