Positive solutions for (k,n−k)(k,n−k) conjugate boundary value problems in Banach spaces

The existence and multiplicity of positive solutions for a integral equation in Banach spaces are obtained. Using these results, we investigate the existence of multiple-positive solutions for (k,n−k)(k,n−k) conjugate boundary value problems. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. This work gives an unified approach applicable to many boundary value problems.