This paper deals with the second-order nonlinear differential equation $(a(t)|x^{\prime }{|}^{p(t)-2}{x}^{\prime }{)}^{\prime }=b(t)|x{|}^{q(t)-2}x$ involving $p(t)$-Laplacian. The existence and the uniqueness of nonoscillatory solutions of this equation in certain classes, which are related with integral conditions, are studied. Moreover, a minimal set for solutions of this equation is introduced as an extension of the concept of principal solutions for linear equations. Obtained results extend the results for equations with $p$-Laplacian.

中文翻译：

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具有 p(t)-拉普拉斯算子的微分方程解的渐近行为

本文处理二阶非线性微分方程$(\mathrm{一个}(吨)|X^{\text{'}}{|}^{p(吨)-2}{X}^{\text{'}}{)}^{\text{'}}=b(吨)|X{|}^{q(吨)-2}X$涉及$p(吨)$-拉普拉斯算子。研究了该方程在与积分条件有关的特定类中非振荡解的存在性和唯一性。此外，引入了该方程解的最小集作为线性方程主解概念的扩展。获得的结果扩展了方程的结果$p$-拉普拉斯算子。