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- W2078013695 abstract "In this work, we consider the higher-order differential equation (1) ( − 1 ) n x ( 2 n ) ( t ) = f ( t , x ( t ) , x ′ ( t ) , … , x ( 2 n − 1 ) ( t ) ) , 0 < t < 1 , subject to one of the following multi-point boundary value conditions: (2) x ( 2 i ) ( 0 ) = x ( 2 i ) ( 1 ) = 0 for i = 0 , 1 , … , n − 1 , or (3) x ( 2 i + 1 ) ( 0 ) = x ( 2 i ) ( 1 ) = 0 for i = 0 , 1 , … , n − 1 , where f ( t , x 0 , x 1 , … , x 2 n − 1 ) is continuous with f ( t , x 0 , x 1 , … , x 2 n − 1 ) ≥ 0 for all t ∈ [ 0 , 1 ] and ( x 0 , x 1 , … , x 2 n − 1 ) ∈ R 2 n . Sufficient conditions for the existence of at least one positive solution of the BVP (1) , (2) and BVP (1) , (3) are established, respectively. The emphasis in this work is on f depending on all higher-order derivatives. Examples are given to illustrate the main results." @default.
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- W2078013695 date "2005-02-01" @default.
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- W2078013695 title "Positive solutions of two-point boundary value problems for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:math>-order differential equations dependent on all derivatives" @default.
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- W2078013695 doi "https://doi.org/10.1016/j.aml.2004.04.009" @default.
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