Displaying similar documents to “On some boundary value problems for second order nonlinear differential equations”

Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Christopher S. Goodrich (2013)

Commentationes Mathematicae Universitatis Carolinae

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We consider the existence of at least one positive solution to the dynamic boundary value problem - y Δ Δ ( t ) = λ f ( t , y ( t ) ) , t [ 0 , T ] 𝕋 y ( 0 ) = τ 1 τ 2 F 1 ( s , y ( s ) ) Δ s y σ 2 ( T ) = τ 3 τ 4 F 2 ( s , y ( s ) ) Δ s , where 𝕋 is an arbitrary time scale with 0 < τ 1 < τ 2 < σ 2 ( T ) and 0 < τ 3 < τ 4 < σ 2 ( T ) satisfying τ 1 , τ 2 , τ 3 , τ 4 𝕋 , and where the boundary conditions at t = 0 and t = σ 2 ( T ) can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.

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.

On a class of m -point boundary value problems

Rodica Luca (2012)

Mathematica Bohemica

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We investigate the existence of positive solutions for a nonlinear second-order differential system subject to some m -point boundary conditions. The nonexistence of positive solutions is also studied.