MULTIPLE POSITIVE SOLUTIONS OF FOURTH-ORDER FOUR-POINT BOUNDARY-VALUE PROBLEMS WITH CHANGING SIGN COEFFICIENT

作者：Fang Zheng^*; Li Chunhong; Bai Chuanzhi

来源：Electronic Journal of Differential Equations, 2008, 159.

• Four-point boundary-value problem
• positive solution
• fixed point on a cone

In this paper, we investigate the existence of multiple positive solutions of the fourth-order four-point boundary-value problems
y((4)) (t) = h(t)g(y(t), y ''(t)), 0 < t < 1,
y(0) = y(1) = 0,
ay ''(xi(1)) - by'''(xi(1)) = 0, cy ''(xi(2)) + dy'''(xi(2)) = 0,
where 0 < xi(1) < xi(2) < 1. We show the existence of three positive solutions by applying the Avery and Peterson fixed point theorem in a cone, here h(t) may change sign on [0, 1].

• 单位
  淮阴师范学院; 江南大学