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On functional integrability of solutions of differential equations with deviating argument. (English) Zbl 0585.34048
Conditions are given for the solutions of the equation \((G_{n- 1}x(t))'+f(t,x(g(t)))=h(t),\) \(t\geq a\), to satisfy \(0<\int^{\infty}_{a}s^ mW(| x(s)|)ds<\infty,\) where \(G_{n-1}x(t)=a_{n-1}(t)(a_{n-2}(t)(...(a_ 1(t)x'(t))'...)')\quad ',\) m is a real number and \(W: {\mathbb{R}}\to {\mathbb{R}}\) (W(\(| u|)\geq 0)\) is a continuous and non-decreasing function.
Reviewer: M.M.Konstantinov
MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C11 Growth and boundedness of solutions to ordinary differential equations
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References:
[1] HRUBINOVÁ A., ŠOLTÉS V.: Asymptotic properties of oscillatory solutions of n-th order differential equations with delayed argument. Zborník vedeckých prác VŠT · Zbl 0583.34062
[2] WERBOWSKI J., WYRWINSKA A.: On functional integrability of solutions of differential equations with deviating argument. Colloquia Mathematica Societatis Janos Bolyai 30. Qualitative Theory of Differential Equations, Szeged (Hungary), 1979, 1045-1059. · Zbl 0486.34052
[3] WYRWINSKA A.: On the functional integrability and asymptotic behaviours of a certain differential equation with delay. Math. Slovaca 33, 1983, 45-51. · Zbl 0526.34053
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