摘要
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.
基金
Supported by National Natural Science Foundation of China(Grant No.11071109)
