Positive solutions for singular second order differential equations with integral boundary conditions

Abstract In this paper, we study the existence of positive solutions for the singular second order integral boundary value problem { u ″ ( t ) + a ( t ) u ′ ( t ) + b ( t ) u ( t ) + c ( t ) f ( u ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = ∫ 0 1 g ( s ) u ( s ) d s , u ( 1 ) = ∫ 0 1 h ( s ) u ( s ) d s , where c ( t ) is allowed to be singular at t = 0 , 1 and f ( u ) may be singular at u = 0 . The existence of positive solutions for the above problem is established by applying the fixed point index theorems under some weaker conditions concerning the first eigenvalue corresponding to the relevant linear operator. The results obtained herein generalize and improve some known results including singular and non-singular cases.

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