Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation
نویسندگان
چکیده
منابع مشابه
Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation
and Applied Analysis 3 (d) if ∫+∞ c ∫ +∞ u uG(s, u)ds du < +∞, then ∞ ∑ j=1 ∫ +∞ t+jτ ∫ +∞ u G (s, u) ds du ≤ 1 τ ∫ +∞ t+τ ∫ +∞ u uG (s, u) ds du < +∞, ∀t ≥ c. (10) Proof. Let [t] denote the largest integral number not exceeding t ∈ R. Note that lim r→+∞ [(r − c) /τ] + 1 r = 1 τ , (11) c + nτ ≤ r < c + (n + 1) τ ⇐⇒ n ≤ r − c τ < n + 1, ∀n ∈ N0. (12) Clearly (12) means that ∞ ∑ j=0 ∫ +∞
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where n ≥ is an integer, τ > , σ ≥ , d > c ≥ , b > a ≥ , r, P ∈ C([t,∞), (,∞)), P ∈ C([t,∞)× [a,b], (,∞)), Q ∈ C([t,∞), (,∞)), Q ∈ C([t,∞)× [c,d], (,∞)), f ∈ C(R,R), f is a nondecreasing function with xf (x) > , x = . The motivation for the present work was the recent work of Culáková et al. [] in which the second-order neutral nonlinear differential equation of the form [ ...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2013
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2013/165382