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Liapunov functionals, fixed points, and stability by Krasnoselskii’s theorem. (English) Zbl 1084.47522

The author uses a modification of Krasnosel’skiń≠’s fixed point theorem [T. A. Burton, Proc. Am. Math. Soc. 124, No. 8, 2383–2390 (1996; Zbl 0873.45003)] to give sufficient conditions for the asymptotic stability of the zero solution of the functional-differential equation \(x'=-a(t)x^3(t)+b(t)x^3(t- r(t))\), where \(r(t)\) need neither be bounded nor differentiable, while \(a\) and \(b\) can be unbounded.

MSC:

47H10 Fixed-point theorems
34K20 Stability theory of functional-differential equations
47N20 Applications of operator theory to differential and integral equations

Citations:

Zbl 0873.45003
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