Existence of positive solutions for [formula omitted]th-order singular semipositone differential equations with Sturm–Liouville boundary conditions

Abstract

This paper studies a class of 2 n th-order singular semipositone differential equations with Sturm–Liouville boundary conditions. Some new results on the existence of C ( 2 n − 2 ) [ 0 , 1 ] positive solutions and C ( 2 n − 1 ) [ 0 , 1 ] positive solutions for this class of differential equations are derived. We obtain some relations between the solutions and Green’s functions.