Multiple positive solutions for nonlinear third order general three-point boundary value problems

Abstract

We consider the third order nonlinear three point boundary value problem,where f : [t 1 , t 3 ]×IR → IR is continuous, t 1 < t 2 < t 3 and α i1 , α i2 , α i3 , i = 1, 2, 3, are real constants. We establish the existence of at least three positive solutions by using well-known LeggettWilliams fixed point theorem and an example is presented.