Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation
نویسندگان
چکیده
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 ∫ +∞
منابع مشابه
Nonlinear oscillation of certain third-order neutral differential equation with distributed delay
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...
متن کاملUncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...
متن کاملExistence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay
...
متن کاملExistence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
متن کاملGlobal Solvability and Mann Iteration Method with Error for a Third Order Nonlinear Neutral Delay Differential Equation (communicated by Agacik Zafer)
This paper intends to investigate the existence of uncountably many bounded positive solutions of a third order nonlinear neutral delay differential equation d dt { r1(t) d dt [ r2(t) d dt ( x(t)− f(t, x(t− σ)) )]} + d dt [ r1(t) d dt g(t, x(p(t))) ] + d dt h(t, x(q(t))) = l(t, x(η(t))), t ≥ t0 in the following bounded closed and convex set Ω(a, b) = { x(t) ∈ C([t0,+∞),R) : a(t) ≤ x(t) ≤ b(t), ...
متن کاملPeriodic solutions for a higher order nonlinear neutral functional differential equation
In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained. Keywords—Neutral functional differential equation, higher order, periodic solution, coincidence degree theory
متن کامل