共查询到20条相似文献,搜索用时 15 毫秒
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Christopher T.H. Baker Yihong Song 《Journal of Computational and Applied Mathematics》2010,234(9):2683-2698
In this paper we discuss the existence of periodic solutions of discrete (and discretized) non-linear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non-linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The “summation” equations studied here can arise as discrete models in their own right but are (as we demonstrate) of a type that arise from the discretization of such integral equations. Our main results are in two parts: (i) results for discrete equations and (ii) consequences for quadrature methods applied to integral equations. The first set of results are obtained using a variety of fixed-point theorems. The second set of results address the preservation of properties of integral equations on discretizing them. The effect of weak singularities is addressed in a final section. The detail that is presented, which is supplemented using appendices, reflects the differing prerequisites of functional analysis and numerical analysis that contribute to the outcomes. 相似文献
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主要讨论带周期边值条件的二维波动方程,利用变分法寻找其周期解,并利用一些特殊的数作为周期使这一方法变得更简单. 相似文献
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Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay
The existence of periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay is obtained by using stability properties of a bounded solution. 相似文献
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Anna Karczewska Carlos Lizama 《Journal of Mathematical Analysis and Applications》2009,349(2):301-310
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main results provide sufficient conditions for strong solutions to stochastic Volterra equations. 相似文献
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Yihong Song 《Journal of Mathematical Analysis and Applications》2006,314(1):174-194
For discrete Volterra equations with or without delay, we obtain several results concerning almost periodic solutions and asymptotically almost periodic solutions under certain conditions. We also investigate the relations among solutions of equations discussed and give an example to illustrate our results. 相似文献
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Systems with past memory (or after-effect), the state of which is given by nonlinear Volterra- type integrodifferential equations with small perturbations, are investigated. The equations depend on functionals in integral form and, in particular, on analytic functionals represented by Fréchet series. The integral kernels can allow for singularities with Abel’s kernel. The stability under persistent disturbances, and the structure of the general solution, are investigated in the neighborhood of zero for an equation with holomorphic nonlinearity assuming asymptotic stability of the trivial solution of the linearized unperturbed equation. Stability in the critical cases (in Lyapunov’s sense) of a single zero root and of pairs of pure imaginary roots for the unperturbed equation is analyzed. 相似文献
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Christopher S. WithersSaralees Nadarajah 《Applied mathematics and computation》2011,218(5):2353-2363
Power series type solutions are given for a wide class of linear and q-dimensional nonlinear Volterra equations on Rp. The basic assumption on the kernel K(x, y) is that K(x, xt) has a power series in x. For example, this holds for any analytic kernel.The kernel may be strongly singular, provided certain constants are finite. One and only one such power series solution exists. Its coefficients are given by a simple iterative formula. In many cases this may be solved explicitly. In particular an explicit formula for the resolvent is given. 相似文献
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Taishan Yi 《Journal of Mathematical Analysis and Applications》2003,286(1):220-229
Consider the difference equation
(∗) 相似文献
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Yihong Song Jingsong Ni Christopher T.H. Baker 《Journal of Difference Equations and Applications》2013,19(3):423-439
The existence of non-negative convergent solutions of discrete Volterra equations is obtained, by using a variety of fixed-point theorems. Examples are given to illustrate the results. 相似文献
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Tomáš Bárta 《Semigroup Forum》2008,76(1):142-148
We show that solutions of Volterra integrodifferential equations are analytic provided the leading operator generates an analytic
semigroup and the convolution kernel is in a space of analytic functions. Similar results have been obtained via Laplace transform,
so far. We show that it is possible to obtain such results using a semigroup approach. 相似文献
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Marian Kwapisz 《Aequationes Mathematicae》1992,43(2-3):191-197
Summary In the paper a discrete analog to the Volterra nonlinear integral equation is discussed. Weighted norms are used to find sufficient conditions that all solutions of such equations are elements of anl
p space.Some generalizations ofl
p spaces are also considered and the corresponding sufficient conditions are established. 相似文献
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We give an overview of results on the existence of periodic solutions of difference equations that have been obtained in the last two decades. The survey covers both ordinary and Volterra difference systems. Some extensions and generalizations of known result are also presented. 相似文献
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An analog of L. Cesari's method for a very general class of evolutionary equations is investigated. A result is proved concerning the coincidence of rotation of a Cesari field with the rotation of a translation operator (on boundaries of naturally corresponding regions), and Galerkin's method of obtaining periodic solutions is studied. The results obtained are new for ordinary differential equations.Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 651–662, June, 1971. 相似文献