A class of 2nth-order singular boundary value problems

Abstract This paper investigates the existence of positive solutions for 2 n th -order ( n > 1 ) singular sub-linear boundary value problems. First of all, we establish the maximal principle and some important lemmas. Then, we define a partial ordering in C 2 n − 2 [ 0 , 1 ] ∩ C 2 n ( 0 , 1 ) and construct lower and upper solutions to give 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. 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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