Nonoscillation of higher order functional differential equations
نویسندگان
چکیده
منابع مشابه
Nonoscillation Criteria for Solutions of Higher-order Functional Difference Equations of Neutral Type
In this paper, we find necessary conditions for every solution of the neutral functional difference equation ∆m−1 ( rn∆(yn − pnyτ(n)) ) + qnG(yσ(n)) = fn to oscillate or to tend to zero as n→∞, where ∆ is the forward difference operator, given by ∆xn = xn+1−xn; and pn, qn, rn are sequences of real numbers with qn ≥ 0, rn > 0. It is supposed that τ(n) and σ(n) are increasing sequences of integer...
متن کاملOscillation and Nonoscillation of Even - Order Nonlinear Delay - Differential Equations
for their oscillatory and nonoscillatory nature. In Eqs. (1) and (2) y("(x) = (d%/dx')y{x), i = 1, 2, • • • , 2n; yr(x) = y(x — t(x))] dy/dx and d2y/dx2 will also be denoted by y' and y" respectively. Throughout this paper it will be assumed that p(x), j(x), t{x) are continuous real-valued functions on the real line (—°°, °°); j(x), p(x) and t(x), in addition, are nonnegative, r(x) is bounded a...
متن کاملOscillation and Nonoscillation Criteria for Second-order Linear Differential Equations
Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 1. Statement of the Problem and Formulation of Basic Results Consider the differential equation u′′ + p(t)u = 0, (1) where p : [0, +∞[→ [0, +∞[ is an integrable function. By a solution of equation (1) is understood a function u : [0,+∞[→] − ∞, +∞[ which is locally absolutely continuous tog...
متن کاملOscillation and Nonoscillation Theorems for a Class of Even-order Quasilinear Functional Differential Equations
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 ...
متن کاملNonoscillation criteria for second-order nonlinear differential equations
Consider the second order nonlinear differential equations with damping term and oscillation’s nature of ( ( ) '( )) ' ( ) '( ) ( ) ( ( )) ( '( )) 0 r t x t p t x t q t f x t k x t 0 t t (1) to used oscillatory solutions of differential equations ( ( ) '( )) ' ( ) ( ( )) ( '( )) 0 t x t t f x t k x t (2) where ( ) t and ( ) t satisfy conditions given in this work paper. Our ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90264-0