On positive solutions for a second order differential system with indefinite weight

In this paper, we consider the existence of positive solutions for a second order differential system - u ? = a ( t ) ? u + h ( t ) f ( u ) , 0 < t < 1 , - ? ? = b ( t ) u , 0 < t < 1 , u ( 0 ) = u ( 1 ) = 0 , ? ( 0 ) = ? ( 1 ) = 0 , where a ( t ) , b ( t ) , h ( t ) change sign. The proof is based on the well-known fixed point theorem of cone expansion and compression.

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