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- W2168713486 abstract "Abstract The second order linear differential equation is considered, where 𝑞 : [0, ∞) → (0, ∞) is continuous, piecewise continuously differentiable, non-decreasing, and lim 𝑡→∞ 𝑞(𝑡) = ∞. A solution 𝑥 0 is called small if lim 𝑡→∞ 𝑥 0 (𝑡) = 0. It is known that the equation always has at least one nontrivial small solution, but, in general, it can have also solutions not small. The Armellini–Tonelli–Sansone Theorem says that if the function 𝑞 grows “regularly” in some sense, then all solutions are small. A generalization of this growth condition is given in terms only of the integral of 𝑞 and . It is proved that the result is a real generalization of the earlier theorems." @default.
- W2168713486 created "2016-06-24" @default.
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- W2168713486 date "2007-06-01" @default.
- W2168713486 modified "2023-09-23" @default.
- W2168713486 title "The Growth Condition Guaranteeing Small Solutions for a Linear Oscillator with an Increasing Elasticity Coefficient" @default.
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- W2168713486 doi "https://doi.org/10.1515/gmj.2007.269" @default.
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