Additive groups connected with asymptotic stability of some differential equations⋆
نویسندگان
چکیده
The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient λq(s), s ∈ [s0,∞) is investigated, where λ ∈ R 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 = Z, S = D (i.e. the set of dyadic numbers), and Q ⊂ S $ R. AMS Subject Classification. 34C10
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