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1. Asymptotic properties of differential equations with advanced argument

Creator:
Čermák, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, functional (nondifferential) equation, advanced argument, and asymptotic behaviour
Language:
English
Description:
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation \[ y^{\prime }(x)=ay(\tau (x))+by(x),\qquad x\in [x_0,\infty ) \] of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution $y(x)$ which behaves in this way.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Oscillation conditions for difference equations with several variable arguments

Creator:
Chatzarakis, George E., Kusano, Takaŝi, and Stavroulakis, Ioannis P.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
difference equation, retarded argument, advanced argument, oscillatory solution, and nonoscillatory solution
Language:
English
Description:
Consider the difference equation ∆x(n) +∑m i=1 pi(n)x(τi(n)) = 0, n ≥ 0 [ ∇x(n) − ∑m i=1 pi(n)x(σi(n)) = 0, n ≥ 1 ] , where (pi(n)), 1 6 i 6 m are sequences of nonnegative real numbers, τi(n) [σi(n)], 1 6 i 6 m are general retarded (advanced) arguments and ∆ [∇] denotes the forward (backward) difference operator ∆x(n) = x(n + 1) − x(n) [∇x(n) = x(n) − x(n − 1)]. New oscillation criteria are established when the well-known oscillation conditions lim sup n→∞ ∑m i=1 ∑n j=τ(n) pi(j) > 1 [ lim sup n→∞ ∑m i=1 σ∑ (n) j=n pi(j) > 1 ] and lim inf n→∞ ∑m i=1 n∑−1 j=τi(n) pi(j) > 1⁄e [ lim inf n→∞ ∑m i=1 σ∑i(n) j=n+1 pi(j) > 1⁄e ] are not satisfied. Here τ (n) = max 1≤i≤m τi(n) [σ(n) = min 1≤i≤m σi(n)]. The results obtained essentially improve known results in the literature. Examples illustrating the results are also given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Oscillation of fourth-order quasilinear differential equations

Creator:
Li, Tongxing, Rogovchenko, Yuriy V., and Zhang, Chenghui
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, quasilinear functional differential equation, delayed argument, and advanced argument
Language:
English
Description:
We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Oscillations of nonlinear difference equations with deviating arguments

Creator:
Chatzarakis, George E. and Dix, Julio G.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
infinite sum condition, retarded argument, advanced argument, oscillatory solution, and nonoscillatory solution
Language:
English
Description:
This paper is concerned with the oscillatory behavior of first-order nonlinear difference equations with variable deviating arguments. The corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public