共查询到20条相似文献,搜索用时 9 毫秒
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X.H. Tang 《Journal of Mathematical Analysis and Applications》2004,289(2):367-378
In this paper, we obtain some oscillation criteria for the first order delay differential equation with distributed delay
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This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to that of the corresponding deterministic delay differential equation. However, boundedness of the second moment is complicated and depends on the stochastic terms. In this paper, the characteristic function of the equation is obtained through techniques of the Laplace transform. From the characteristic equation, sufficient conditions for the second moment to be bounded or unbounded are proposed. 相似文献
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Katia A.G. Azevedo Marta C. Gadotti Luiz A.C. Ladeira 《Nonlinear Analysis: Theory, Methods & Applications》2007
We discuss the existence of periodic solutions to a system of differential equations with distributed delay which shows a certain type of symmetry. For this, such solutions are related to the solutions of a system of second-order ordinary differential equations. 相似文献
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赵晓强 《应用数学学报(英文版)》1993,9(4):328-334
In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R~n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t). 相似文献
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Maoan Han 《Journal of Differential Equations》2003,189(2):396-411
In this paper we develop Kaplan-Yorke's method and consider the existence of periodic solutions for some delay differential equations. We especially study Hopf and saddle-node bifurcations of periodic solutions with certain periods for these equations with parameters, and give conditions under which the bifurcations occur. We also give application examples and find that Hopf and saddle-node bifurcations often occur infinitely many times. 相似文献
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In this paper, we consider the existence of periodic solutions for second-order differential delay equations. Some existence results are obtained using Malsov-type index and Morse theory, which extends and complements some existing results. 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(2):430-437
In this note we establish the existence of pseudo-almost periodic solutions for a non-autonomous partial neutral functional differential with unbounded delay. We apply our abstract results to establish the existence of this type of solutions for a neutral differential equation which arises in the theory of heat conduction in materials with fading memory. 相似文献
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In this paper, we study almost periodic logistic delay differential equations. The existence and module of almost periodic solutions are investigated. In particular, we extend some results of Seifert in [G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000) 451–458]. 相似文献
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The purpose of this paper is to study the oscillation of a certain class of third-order neutral differential equations with continuously distributed delay. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero. 相似文献
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Wieslaw Krawcewicz Jianshe Yu Huafeng Xiao 《Journal of Fixed Point Theory and Applications》2013,13(1):103-141
By applying the method based on the usage of the equivariant gradient degree introduced by G?ba (1997) and the cohomological equivariant Conley index introduced by Izydorek (2001), we establish an abstract result for G-invariant strongly indefinite asymptotically linear functionals showing that the equivariant invariant ${\omega(\nabla \Phi)}$ , expressed as that difference of the G-gradient degrees at infinity and zero, contains rich numerical information indicating the existence of multiple critical points of ${\Phi}$ exhibiting various symmetric properties. The obtained results are applied to investigate an asymptotically linear delay differential equation $$x\prime = - \nabla f \big ({x \big (t - \frac{\pi}{2} \big )} \big ), \quad x \in V \qquad \quad (*)$$ (here ${f : V \rightarrow \mathbb{R}}$ is a continuously differentiable function satisfying additional assumptions) with Γ-symmetries (where Γ is a finite group) using a variational method introduced by Guo and Yu (2005). The equivariant invariant ${\omega(\nabla \Phi) = n_{1}({\bf H}_{1}) + n_{2}({\bf H}_{2}) + \cdots + n_{m}({\bf H}_{m})}$ in the case n k ≠ 0 (for maximal twisted orbit types (H k )) guarantees the existence of at least |n k | different G-orbits of periodic solutions with symmetries at least (H k). This result generalizes the result by Guo and Yu (2005) obtained in the case without symmetries. The existence of large number of nonconstant periodic solutions for (*) (classified according to their symmetric properties) is established for several groups Γ, with the exact value of ${\omega(\,\nabla \Phi)}$ evaluated. 相似文献
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Existence of almost periodic solutions to delay differential equations with Lipschitz nonlinearities
William Layton 《Journal of Differential Equations》1984,55(2):151-164
Differential equations whose nonlinearities depend upon both x(t) and x(t ? τ) arise in many settings. In this paper equations of this form subject to periodic and almost periodic forcing are studied: x′(t) + g(x(t), x(t ? τ)) = e(t), ?∞ < t < ∞. (E) A nonresonance type condition is found under which it is shown that (E) will have a unique Besicovitch almost periodic solution for any Besicovitch almost periodic forcing term e(t). These results are then generalized to systems of equations of the same form as (E). These results hold without any small parameter type restriction upon g. 相似文献
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T. L. Sabatulina 《Russian Mathematics (Iz VUZ)》2010,54(11):44-55
We obtain unimprovable sufficient conditions for the positivity of the Cauchy function for differential equation with distributed
delay. Based on these conditions, we study some asymptotic properties of solutions of the Hutchinson-Wright equation, the
Lasota-Wazevska equation, and the Nicholson equation. 相似文献