نتایج جستجو برای: second order nonlinear neutral delay partialdifference equation
تعداد نتایج: 1906622 فیلتر نتایج به سال:
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...
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,...
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 ∫ +∞
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))...
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...
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...
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.
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...
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