Gaps between zeros of second-order half-linear differential equations

Saker S.H.; Agarwal R.P.; ORegan D.

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Gaps between zeros of second-order half-linear differential equations

机译：二阶半线性微分方程零点之间的间隙

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In this paper, for second order half-linear differential equations, we will establish some new inequalities of Lyapunov's type. These inequalities give results related to the spacing between consecutive zeros of a solution and the spacing between a zero of a solution and/or a zero of its derivative. The results also yield conditions for disfocality, disconjugacy and lower bounds for an eigenvalue of a boundary value problem. The main results will be proved by making use of some generalizations of Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.

机译：在本文中，对于二阶半线性微分方程，我们将建立Lyapunov型的一些新的不等式。这些不等式给出的结果与解的连续零之间的间距以及解的零和/或其导数的零之间的间距有关。结果还为边值问题的特征值产生了散焦，模糊和下界的条件。主要结果将通过使用Opial和Wirtinger型不等式的一些推广来证明。考虑一些例子来说明主要结果。

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《Applied mathematics and computation》 |2012年第3期|共11页
作者
Saker S.H.; Agarwal R.P.; ORegan D.;
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正文语种 eng
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关键词
Disfocality; Half-linear differential equations; Nonoscillation; Opial's inequality;

机译：散焦;半线性微分方程;无振动;阿不等式;

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1. Gaps between zeros of second-order half-linear differential equations [J] . Saker S.H., Agarwal R.P., ORegan D. Applied mathematics and computation . 2012,第3期

机译：二阶半线性微分方程零点之间的间隙
2. Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations [J] . Shan Shi, Zhenlai Han 应用数学与计算数学学报(英文) . 2021,第003期

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6. Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon’s data plot then specify a unique differential equation for it [O] . Gordon R Kepner 2014

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7. On the number of zeros of principal solutions to second-order half-linear ordinary differential equations (Mathematical Models in Functional Equations) [O] . Kusano Takashi, Naito Manabu 2000

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Gaps between zeros of second-order half-linear differential equations

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