Abstract
This paper investigates the existence of positive solutions of singular sub-linear boundary value problems for fourth-order and second-order differential equation systems. First of all, we establish some important Lemmas. Then, we define a partial ordering in C 2[ a, b] ∩ C 4( a, b) × C[ a, b] ∩ C 2( a, b) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C 2[0, 1] × C[0, 1] positive solutions as well as C 3[0, 1] × C 1[0, 1] positive solutions. Our nonlinearity f( t, x 1, x 2, x 3), g( t, x 1, x 2) may be singular at x 1 = 0, x 2 = 0, x 3 = 0, t = 0 and or t = 1.
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