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Start Over Creator Kusano, Takaŝi

1. Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Creator:
Kusano, Takaŝi and Marušiak, Pavol
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
quasiiinear differential equations of neutral type, oscillatory, non-oscillatory solutions, and Schauder-Tychonoff fixed point theorem
Language:
English
Description:
This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasiiinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as t → ∞.
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