Characterization of non-disconjugacy for a one parameter family of nth-order linear differential equations. (March 2017) - Cabada, Alberto; Saavedra, Lorena
Abstract: The aim of this paper is to obtain different criteria which ensure that the one parameter family of n th -order linear differential equations, given by the following expression (1) T n [ M ] u ( t ) ≡ u ( n ) ( t ) + a 1 ( t ) u ( n − 1 ) ( t ) + ⋯ + a n − 1 ( t ) u ′ ( t ) + ( a n ( t ) + M ) u ( t ) = 0, t ∈ I ≡ [ a, b ], is not disconjugate for every M ∈ R . Three different sufficient criteria, which warrant that such a property holds, are presented. Moreover, a characterization of this property is given. To finish the paper, there are shown three examples where the different criteria are applied.