The solutions for Semipositone (k,n-k) conjugate boundary value problems

Abstract

©, 2015, Chinese Academy of Sciences. All right reserved.We consider the existence of positive solutions to the following semiposi-tone (k,n-k) conjugate boundary value problems (SCBVP): [Formula is presented] where n=2, 1<k<n-1. The nonlinear function f may change sign for 0 < t < 1, i.e., we allow that the nonlinear term f is both semipositone and lower unbounded. Without making any monotone-type assumption, by using the fixed-point index theory, the existence of positive solution and many positive solutions are obtained.