Extreme and moderate solutions of nonoscillatory second order half-linear differential equations
Extreme and moderate solutions of nonoscillatory second order half-linear differential equations
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DOI：
10.4064/ap201216-12-8
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发表时间：
2021
影响因子：
0.5
通讯作者：
J. Jaros;T. Kusano;T. Tanigawa
中科院分区：
文献类型：
--
作者：
J. Jaros;T. Kusano;T. Tanigawa
。建立了二阶半线性微分方程的存在和渐近理论，其中 α > 0 是常数，p ( t ) 和 q ( t ) 是 [ a, ∞ ) 上的正连续函数，其中与 (A) 相关的一对广义 Riccati 微分方程发挥着至关重要的作用。该理论的一个重要部分是构造 (A) 的非振荡解 x ( t )，并根据 (R1) 的解 u ( t ) 或 (R2) 的解 v ( t ) 享受显式指数积分表示。
. An existence and asymptotic theory is built for second order half-linear differential equations of the form where α > 0 is constant and p ( t ) and q ( t ) are positive continuous functions on [ a, ∞ ) , in which a crucial role is played by a pair of the generalized Riccati differential equations associated with (A). An essential part of the theory is the construction of nonoscillatory solutions x ( t ) of (A) enjoying explicit exponential-integral representations in terms of solutions u ( t ) of (R1) or in terms of solutions v ( t ) of (R2).