The Existence Of Multiple Positive Solutions For Second-Order Multi-Point Boundary Value Problems In Banach Spaces

In this paper, by using fixed point theorems of strict set contraction mapping, we study two kinds of boundary value problems for compact type conditions in Banach spaces. In the first part, we obtain the existence of three positive solutions for second-order n-point boundary value problem in Banach spaces by using a generalized fixed point theorem. In the second part, we make use of fixed point theorem of conic expansion and compression to prove the existence of two positive solutions in Banach spaces for second-order four-point boundary value problem whose coefficient of nonlinear term is allowed to change sign. In the last of each part, we also give an example to demonstrate the availablity of our results.