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1.
By using the Riccati technique and the technique, new oscillation criteria are obtained for the second order matrix differential system(P(t)Y′(t))′ r(t)P(t)Y′(t) Q(t)Y(t) = 0, t≥t0.These results in the present paper generalize and improve many known conclusions. Furthermore, some results are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. In particular, our results complement a number of existing results and handle the ease that is not covered by the known criteria.  相似文献   

2.
非线性中立型延迟微分方程稳定性分析   总被引:16,自引:1,他引:15  
王晚生  李寿佛 《计算数学》2004,26(3):303-314
This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equations(NDDEs) of the general form y′(t)=F(t,y(t),G(t,y(t-τ-(t)),y′(t-τ-(t)))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y′(t)=F(t,y(t),G(t,y(t-τ-(t)),y′(t-τ-(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.  相似文献   

3.
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' p(t)(y'(t))σ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.  相似文献   

4.
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form (r2(t)((r1(t)(y′(t))α)′)β)′+ q(t)y~γ(σ(t)) = 0, t ≥ t_0 0, where ∫~∞ r_1~(-α/1)(s)ds ∞ and ∫~∞ r_2~(-1/β)(s)ds ∞. The criteria in this paper improve and complement some existing ones. The results are illustrated by two Euler-type differential equations.  相似文献   

5.
戚仕硕 《东北数学》2002,18(1):63-72
The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:{u′″(t)=a(t)f(u(t)),t∈[0,1],;a1u(0)-b1u′(0)-c1u(1) d1u′(1)=0,;a2u″(0)-b2u′″(0)=c2u″(1) d2u′″(1)=0.Several existence theorems on multiple positive solutions to the problems are obtained,ad some examples are given to show the validity of these results.  相似文献   

6.
The purpose of this paper is to give some sufficient conditions on / and g for ensuring that all solutions or all bounded solutions of general second order functional differential equation 〔r(t)g(y′(t))〕′+ f(t,y(t),y(p(t)),y′(t),y′(q(t)))=0 are oscillatory, or it has at least one bounded nonoscillatory solution.  相似文献   

7.
Oscillation criteria for the delay differential equationx′(t)+p(t)x(t-т(t))=0,where p, т are non-negative real-valued continuous functions are investigated inthe case when the numbers k=integral from n=t-т(t) to t(p(s)ds),L=integral from n=t-т(t) to t(p(s)ds)satisfy 0≤k<1/e and 1/e≤L<1. The present result improves almost allresults of the literature concerning it. Furthermore, it is established that allsolutions of the odd-order neutral delay differential equation(x(t)-px(t-т))~(n)+Q(t)x(t-σ)=0,where 0≤p<1,т,σ∈(0,∞)and Q(t)≥0,are oscillatory ifintegral from n=t-σ to t ((t-s)~(n-1)Q(s)ds>(1/e)(1-p)(n-1))!.This result generalizes a theorem of Gopalsamy et. al (Czech. Math. J., 42(1992),313-323)and also extends a very well-known result of Ladas (ApplicableAnalysls, 9(1979),93-98).  相似文献   

8.
By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and some sufficient condition which ensures that all of the solutions of the aboveequation are oscillatory are obtained.  相似文献   

9.
The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.  相似文献   

10.
孙继涛 《数学季刊》1993,8(1):40-43
In this paper,the existence of nonconstant oscillating periodic solution of differential difference e-quation with n time lags is stutied:x′(t)=-g(x(t))[f(x(t-τ1)) f(x(t-τ2)) … f(x(t-τn))] the results of Paper[1-6] are extended and improved.  相似文献   

11.
We study a system(D)x′=F(t,x t) of functional differential equations, together with a scalar equation(S)x′=−a(t)f(x)+b(t)g(x(t−h)) as well as perturbed forms. A Liapunov functional is constructed which has a derivative of a nature that has been widely discussed in the literature. On the basis of this example we prove results for (D) on asymptotic stability and equi-boundedness. Supported in part by NSF of China, Key Project # 19331060  相似文献   

12.
We obtain 3/2-condition for global attractivity to occur in the “food-limited” type functional differential equationx′ (t) + [1 +x(t)][1 −cx(t)]F(t, x(·)) = 0. These results contain and improve all corresponding theorems in literature.  相似文献   

13.
This paper gives conditions ensuring the existence for an initial value (x 0,v 0) of a solution to the second order differential inclusionx″(t) ∈F[x(t),x′(t)],x(0)=x 0,x′(0)=v 0 such thatx(t)K for allt whereK is a nonempty given subset ofR n .   相似文献   

14.
Let E and F be Banach spaces, f: UEF be a map of C r (r ⩾ 1), x 0U, and ft (x 0) denote the FréLechet differential of f at x 0. Suppose that f′(x 0) is double split, Rank(f′(x 0)) = ∞, dimN(f′(x 0)) > 0 and codimR(f′(x 0)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x 0) near x 0. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators, i.e., x 0 is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the conclusion of the theorem to be held is given.   相似文献   

15.
By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system
(P(t)X'(t))' + R(t)X'(t) + Q(t)X(t) =0, t ≥ to 〉 0
where P(t), R(t), Q(t) are n × n real continuous matrix functions, P(t) and R(t) are commutative. Theresults improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper.  相似文献   

16.
For given , c < 0, we are concerned with the solution f b of the differential equation f ′′′ + ff ′′ + g(f ′) = 0 satisfying the initial conditions f(0) = a, f ′ (0) = b, f ′′ (0) = c, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists b * > 0 such that f b exists on [0, + ∞) and is such that as t → + ∞, if and only if b ≥ b *. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.   相似文献   

17.
LetM(z)=z n +…,N(z)=z n +… be analytic in the unit disc Δ and let λ(z)=N(z)/zN′(z). The classical result of Sakaguchi-Libera shows that Re(M′(z)/N′(z))<0 implies Re(M(z)/N(z))>0 in Δ whenever Re(λ(z))>0 in Δ. This can be expressed in terms of differential subordination as follows: for anyp analytic in Δ, withp(0)=1,p(z)+λ(z)zp′(z)<1+z/1−z impliesp(z)<1+z/1−z, for Reλ(z)>0,z∈Δ. In this paper we determine different type of general conditions on λ(z),h(z) and ϕ(z) for which one hasp(z)+λ(z)zp′(z)<h(z) impliesp(z)<ϕ(z)<h(z) z∈Δ. Then we apply the above implication to obtain new theorems for some classes of normalized analytic funotions. In particular we give a sufficient condition for an analytic function to be starlike in Δ.  相似文献   

18.
Let A>0 be an unbounded self-adjoint operator in a Hilbert space H. In the Hilbert space H1=L2 (0, π; H) we study the spectrum of the differential equations−y″(x)+Ay=λy, y (0)=y(π)=0,−y″(x)+Ay=λy, y′(0) =y′(π)=0. We find the principal terms of the asymptotics of the functions N(λ) for these problems and we ascertain the conditions under which they are asymptotically not equivalent. Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 209–212, February, 1977.  相似文献   

19.
It is proved that (elementary) Chevalley groups G π(Φ,K) and G π′(Φ′,K′) (or E π(Φ,K) and E π′(Φ′,K′)) over infinite fields K and K′ of characteristic different from 2, with weight lattices Λ and Λ′, respectively, are elementarily equivalent if and only if the root systems Φ and Φ′ are isomorphic, the fields K and K′ are elementarily equivalent, and the lattices Λ and Λ′ coincide. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 29–77, 2006.  相似文献   

20.
We establish conditions of asymptotic stability for all solutions of the equation X n+1=F(X n ), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given. Ukrainian Academy of the Water Industry, Rovno. Translated from Ukrainskii Matematicheskii zhurnal, Vol. 49, No. 7, pp. 970–980. July, 1997.  相似文献   

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