DOI: 10.36347/sjpms

Pages: 289-299

The nonlinear (k,n  k)conjugate boundary problem ( 1) ( ) ( , ( )), (0) (1) 0,     n k n i j  y x f x y x y y ( ) ( ) ( ) 0 1,k 1,       i k j n is studied in this paper, where 0  x 1, n 1 0  k  n . The upper and lower boundary of the Green’s function and derivative estimate are given, the existence result of positive solution for the problem is proved by using Krasnoselskii fixed point theorem in cones