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Positive solutions for systems of generalized three-point nonlinear boundary value problems

Johnny HendersonSotiris K. NtouyasIoannis K. Purnaras — 2008

Commentationes Mathematicae Universitatis Carolinae

Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u ' ' + λ a ( t ) f ( v ) = 0 , v ' ' + λ b ( t ) g ( u ) = 0 , for 0 < t < 1 , and satisfying, u ( 0 ) = β u ( η ) , u ( 1 ) = α u ( η ) , v ( 0 ) = β v ( η ) , v ( 1 ) = α v ( η ) . A Guo-Krasnosel’skii fixed point theorem is applied.

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