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Displaying similar documents to “Multiple positive solutions for singular quasilinear multipoint BVPs with the first-order derivative.”

Existence of multiple positive solutions of n th -order m -point boundary value problems

Sihua Liang, Jihui Zhang (2010)

Mathematica Bohemica

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The paper deals with the existence of multiple positive solutions for the boundary value problem ( ϕ ( p ( t ) u ( n - 1 ) ) ( t ) ) ' + a ( t ) f ( t , u ( t ) , u ' ( t ) , ... , u ( n - 2 ) ( t ) ) = 0 , 0 < t < 1 , u ( i ) ( 0 ) = 0 , i = 0 , 1 , ... , n - 3 , u ( n - 2 ) ( 0 ) = i = 1 m - 2 α i u ( n - 2 ) ( ξ i ) , u ( n - 1 ) ( 1 ) = 0 , where ϕ : is an increasing homeomorphism and a positive homomorphism with ϕ ( 0 ) = 0 . Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.