Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations
Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations
复制标题
一类四阶拟线性函数微分方程的振荡和非振荡定理
DOI：
10.32917/hmj/1150997976
复制
发表时间：
2003
影响因子：
0.2
通讯作者：
T. Tanigawa
中科院分区：
文献类型：
--
作者：
T. Tanigawa
我们关注 (|y(n)(t)|α sgn y(n)(t))(n) + q(t)|y(g(t))|β sgn y(g(t))= 0 类型的偶次拟线性泛函微分方程解的振荡和非振荡行为，其中 α 和 β 是正常数，g(t) 和 q(t) 是正连续函数[0,∞)，g(t) 是连续可微函数，使得 g′(t) > 0，limt→∞ g(t)=∞。我们首先给出具有特定渐近行为的非振荡解存在的标准，然后通过将上述方程与相关微分方程进行比较，在不偏离参数的情况下推导出所有解都是振荡的条件（充分以及必要和充分）。
We are concerned with the oscillatory and nonoscillatory behavior of solutions of evenorder quasilinear functional differential equations of the type (|y(n)(t)|α sgn y(n)(t))(n) + q(t)|y(g(t))|β sgn y(g(t))= 0, where α and β are positive constants, g(t) and q(t) are positive continuous functions on [0,∞), and g(t) is a continuously differentiable function such that g′(t) > 0, limt→∞ g(t)=∞. We first give criteria for the existence of nonoscillatory solutions with specific asymptotic behavior, and then derive conditions (sufficient as well as necessary and sufficient) for all solutions to be oscillatory by comparing the above equation with the related differential equation without deviating argument.