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Abstract This article deals with integral boundary value problems of the second-order differential equations { u ″ ( t ) + a ( t ) u ′ ( t ) + b ( t ) u ( t ) + f ( t , u ( t ) ) = 0 , t ∈ J + , u ( 0 ) = ∫ 0 1 g ( s ) u ( s ) d s , u ( 1 ) = ∫ 0 1 h ( s ) u ( s ) d s , $$\left \{ \textstyle\begin{array}{lcl} u''(t)+a(t)u'(t)+b(t)u(t)+f(t,u(t))=0,\quad t\in J_{+},\\ u(0)= \int_{0}^{1}g(s)u(s)\,\text{d}s,\qquad u(1)=\int _{0}^{1}h(s)u(s)\,\text{d}s, \end{array}\displaystyle \right .$$ where a ∈ C ( J ) $a\in C(J)$ , b ∈ C ( J , R − ) $b\in C(J, R_{-})$ , f ∈ C ( J + × R + , R + ) $f\in C(J_{+}\times R_{+}, R^{+})$ and g , h ∈ L 1 ( J ) $g, h\in L^{1}(J)$ are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity f permits the singularity on the space variable.