The existence of symmetric positive solutions for some nonlinear equation systems
Abstract In this paper, the existence of symmetric positive solutions of the following boundary value problem: ( ϕ p 1 ( u ′ ) ) ′ + a 1 ( t ) f ( u , v ) = 0 , 0 t 1 , ( ϕ p 2 ( v ′ ) ) ′ + a 2 ( t ) g ( u , v ) = 0 , 0 t 1 , u ( 0 ) - α u ′ ( ξ ) = 0 , u ( 1 ) + α u ′ ( η ) = 0 , v ( 0 ) - α v ′ ( ξ ) = 0 , v ( 1 ) + α v ′ ( η ) = 0 , is studied, where ϕ p i ( s ) = | s | p i - 2 s , p i > 1 . We show the sufficient conditions for the existence of symmetric positive solutions by using a fixed point index theorem in cones.