Existence of positive solutions for 2nth-order singular sublinear boundary value problems☆

Abstract This paper investigates the existence of positive solutions for 2nth-order ( n > 1 ) singular sub-linear boundary value problems. A necessary and sufficient condition for the existence of C 2 n − 2 [ 0 , 1 ] as well as C 2 n − 1 [ 0 , 1 ] positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity f ( t , x 1 , x 2 , … , x n ) may be singular at x i = 0 , i = 1 , 2 , … , n , t = 0 and/or t = 1 .

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