Abstract
In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions - x ″ = f ( t , y ) , - y ″ = g ( t , x ) , α x ( 0 ) - β x ′ ( 0 ) = δ x ( 1 ) + γ x ′ ( 1 ) = 0 , y ( 0 ) = ay ( ξ 1 ) , y ( 1 ) = by ( ξ 2 ) , where 0 < ξ 1 < ξ 2 < 1 , α , β , δ , γ , a , b are nonnegative constants such that ρ = β γ + α γ + α δ > 0 . By structuring upper and lower solution and using Schauder fixed point theorem, a necessary and sufficient condition for the existence of positive solutions is established. An example is worked out to illustrate our main result.
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