Multiple positive solutions for a class of nonlinear four-point boundary value problem with <Emphasis Type="Italic">p</Emphasis>-Laplacian

This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian: where φ(x) = |x| ^p−2 x, p > 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given. Sponsored by the Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).