Existence of positive solutions for th-order -Laplacian singular sublinear boundary value problems

This paper investigates the existence of positive solutions for n th-order ( n ≥ 3 ) p -Laplacian singular sub-linear boundary value problems. A necessary and sufficient condition for the existence of S p n − 1 positive solutions is given by constructing lower and upper solutions and with the comparison theorem. Our nonlinearity f ( t , x 1 , x 2 , … , x n − 1 ) may be singular at x i = 0 , i = 1 , 2 , … , n − 1 , t = 0 and/or t = 1 .