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Additive groups connected with asymptotic stability of some differential equations

Árpád Elbert (1998)

Archivum Mathematicum

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient λ 2 q ( s ) , s [ s 0 , ) is investigated, where λ and q ( s ) is a nondecreasing step function tending to as s . Let S denote the set of those λ ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that S is an additive group. Four examples are given with S = { 0 } , S = , S = 𝔻 (i.e. the set of dyadic numbers), and S .

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