نتایج جستجو برای: second order nonlinear neutral delay partialdifference equation

تعداد نتایج: 1906622  

2013
Zhenyu Guo Min Liu

A system of second-order nonlinear neutral delay differential equations ( r1(t) ( x1(t) + P1(t)x1(t− τ1) )′)′ = F1 ( t, x2(t− σ1), x2(t− σ2) ) , ( r2(t) ( x2(t) + P2(t)x2(t− τ2) )′)′ = F2 ( t, x1(t− σ1), x1(t− σ2) ) , where τi > 0, σ1, σ2 ≥ 0, ri ∈ C([t0,+∞),R), Pi(t) ∈ C([t0,+∞),R), Fi ∈ C([t0,+∞)× R2,R), i = 1, 2 is studied in this paper, and some sufficient conditions for existence of nonosc...

2014
Zeqing Liu Ming Jia Jeong Sheok Ume Shin Min Kang Sergey V. Zelik

and Applied Analysis 3 where τ, p, g : R → R are continuous functions, B, δ, C are constants, τ and p are T -periodic, C/ 0, |B|/ 1, and T > 0. Zhou and Zhang 8 extended the results in 1 to the higher-order neutral functional differential equation with positive and negative coefficients: d dtn [ x t px t − τ ] −1 n 1 P t x t − σ −Q t x t − δ 0, t ≥ t0, 1.9 where p ∈ R \ {±1}, τ, σ, δ ∈ R and P,...

2014
Zeqing Liu Ling Guan Sunhong Lee Shin Min Kang Jifeng Chu

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 ∫ +∞

2011
Da-Xue Chen Guang-Hui Liu

Received: November 24, 2010 Accepted: December 10, 2010 doi:10.5539/jmr.v3n2p193 This work was supported by the Science and Technology Program of Hunan Province of P. R. China (Grant No. 2010FJ6021). Abstract We investigate the bounded oscillation of the second-order nonlinear neutral delay dynamic equation with oscillating coefficients ( r(t) ∣∣∣∣[x(t) + p(t)x(τ(t))]Δ∣∣∣∣α−1[x(t) + p(t)x(τ(t))...

2015
Qi Li Rui Wang Feng Chen Tongxing Li

By a solution to (.), we mean a function x ∈ C([Tx,∞),R), Tx ≥ t which has the property r(z′)α ∈ C([Tx,∞),R) and satisfies (.) on the interval [Tx,∞). We consider only those solutions of (.) which satisfy condition sup{|x(t)| : t ≥ T} >  for all T ≥ Tx and assume that (.) possesses such solutions. As usual, a solution of (.) is called oscillatory if it has arbitrarily large zeros o...

2006
XIAO-BAO SHU YUAN-TONG XU

where τ, σ , and c are real constants with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T-periodic function for t > 0 and, for an arbitrary bounded domain D ⊂ R, g(t,x) is a Lipschitzfunction on [0,T]×D. Moreover, p ∈ C(R,R), p(t +T) = p(t) and ∫ T 0 p(t)dt = 0. They obtained sufficient conditions which guarantee the existence of at least one T-periodic solution for the above system. However, for the exi...

2011
E. THANDAPANI

In this paper the authors classified all solutions of the following equation ∆ ( an ( ∆(xn + cnxn−k) )α) + pnf(xn−l) − qng(xn−m) = 0 into four classes and obtain conditions for the existence/nonexistence of solutions in these classes. Examples are provided to illustrate the results.

1989
YANG KUANG ALAN FELDSTEIN V. Lakshmikantham

Sufficient conditions are obtained for the boundedness of solutions of the non-linear nonautonomous neutral equation i(t)=r(f)x(t)(a(f)-.x(t-1)-c(/).?(t-1)), which arise in a " food-limited " population model. This partially answers a recent open question proposed The nonlinear neutral delay logistic equation was first introduced and extensively discussed in [6], dx(t)-=i(t)=rx(t)(l-(x(t-)+ci(t...

Journal: :Computers & Mathematics with Applications 2006

Journal: :Journal of Mathematical Analysis and Applications 1999

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