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1.
In this paper we study the oscillation of the solutions of higher-order functional differential equations, and have given the new integral conditions when equation (1) is oscillatory and extended some known results.x(n)(t) p(t)x(g(t)) = 0, (1)where n is even number, p(t) ∈ C(R, [0, ∞)), g(t) ∈ C(R; R), g(t) f55 t,.  相似文献   

2.
In a recent paper of Dhongade, U. D. and Deo, S. G.^[2], the well-known improtant integral inequality due to Bihari^[1] was generalized to the case of haying finite terms of nonlinear integral functionals. Certainly, the generalizations of this type are very useful in treating many problems. Unfortunately the theorems given in [2] are not quite correct. The purpose of the present paper is first to prove the validity of another generalization of Bihari’s inequality, which corrects and extends all of the results in [2], and then as a further application of the obtained inequality, we consider here the perturbations of nonlinear Yolterra integral equations by combining with the nonlinear variation of constants formula established by Brauer, F.^[5] for the Yolterra equations.  相似文献   

3.
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.  相似文献   

4.
A theory of a class of higher order singular integral under the operator(Lf)(u)=1/(ū [ū1 f u 1(u) 1 f ū1(u)+f(u)] is given.We transform the higher order singular integral to a usual Cauchy integral,extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case,and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.  相似文献   

5.
We consider the multidimensional abstract linear integral equation of Volterra type x(t) (*)∫Rtα(s)x(s)ds=f(t),t∈R,(1)as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Bauach space-valued defined on a compact interval R of R^n Rt is a subinterval of R depending on t ∈ R and (*) f denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems, The Henstock integral setting enables us to consider highly oscillating functions.  相似文献   

6.
An important contribution in the development of nonlinear analysis was given by Leray and Schauder. In paper [21] they extended the Brouwer degree to compact continuous fields (i. e. compact continuous perturbations of the identity) and consequently provided a very powerful tool for the investigation of various problems of nonlinear differential equations and nonlinear integral equations. The detailed report of the Leray-Schauder degree and its applications can be found in many books, including [20, 23, 7], to mention only a few.  相似文献   

7.
1. IntroductionWienerHopf equations are integral equations defined on the haif line:where rr > 0, a(.) C L1(ro and g(.) E L2(at). Here R = (--oo,oo) and ty [0,oo). Inou-r discussions, we assume that a(.) is colljugate symmetric, i.e. a(--t) = a(t). WienerHop f equations arise in a variety of practical aPplicatiolls in mathematics and ellgineering, forinstance, in the linear prediction problems fOr stationary stochastic processes [8, pp.145--146],diffuSion problems and scattering problems […  相似文献   

8.
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.  相似文献   

9.
戚仕硕 《东北数学》2000,16(3):329-338
In recent years, the research in integral equations in Banach spaces has achieved many results (refer to [1], [2], [3] etc.). It is well known that, generally, one must first establish the comparison theorem before applying the method of (coupled) lower and upper (quasi)solutions to investigate the (quasi)solutions of integral equations. This can be easily done for Volterra integral equations, but seems impossible for the cases of Fredholm type. Though [3] avoided the establishment of…  相似文献   

10.
THE SINGULARLY PERTURBED PROBLEM FOR COMBUSTION REACTION DIFFUSION   总被引:65,自引:0,他引:65  
1. IntroductionThe anchor discussed a class of problems for the nonlinear ordinary differential equations(of. [1-3]) and the reaction dimsion equations (of. [4-7]).Now we consider a model of the combustion reaction decision problem as follows:where y is a density of combustion flame, s denotes the rate of diffusion effect for reactionspeed, whiCh is a small positive parameter, t is a position of combustion, functions y - t andy t are the positions of the matter for fuel and chide respectivel…  相似文献   

11.
周昱  高明哲 《数学杂志》2011,31(3):575-581
本文研究Hilbert积分不等式的推广问题.利用引入参数和对数积分核函数,建立了一种新的Hilbert型积分不等式,证明了用Euler数和π来表示的常数因子是最佳的,推广了经典的Hilbert积分不等式.  相似文献   

12.
Motivated by an integral inequality conjectured by W. Walter, we prove some general integral inequalities on finite intervals of the real line. In addition to supplying new proofs of Walter's conjecture, the general inequalities furnish a reverse Jensen inequality under appropriate conditions and provide generalizations of Chebyshev's integral inequality.  相似文献   

13.
By using some real analysis techniques, we study the structural characteristics of a multi‐parameter Hilbert‐type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert‐type integral inequalities with simple form by choosing suitable parameter values.  相似文献   

14.
利用一类积分不等式以及参数变易法,Jensen不等式,给出了更为一般的中立型时滞微分系统的Lyapunov稳定性的判别准则,推广和改进了一些文献中有关中立型微分方程的Lyapunov稳定性的结论.  相似文献   

15.
研究了带积分核函数和参数λ(λ〉1)的Hardy-Hilbert型不等式,并利用加强的Hlder’s不等式对Hardy-Hilbert不等式作了改进,建立了一些新的不等式.  相似文献   

16.
新优化的Hilbert积分不等式   总被引:4,自引:0,他引:4  
推广、改进并给出了某些新的重要Hilbert积发不等式。  相似文献   

17.
The aim of this paper is to establish some new partial integral inequalities in two independent variables which can be used in the analysis of a class of nonlinear non-self-adjoint hyperbolic partial integrodifferential equations. An elementary method of reducing the integral inequality to a second-order partial differential inequality and then integrating it by Riemann's method is used to establish our results.  相似文献   

18.
We prove some Lorentz-type estimates for the average in time of suitable geodesic interpolations of probability measures, obtaining as a by product a new estimate for transport densities and a new integral inequality involving Wasserstein distances and norms of gradients. This last inequality was conjectured in a paper by S. Steinerberger.  相似文献   

19.
There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.  相似文献   

20.
关于Hilbert积分不等式新的改进和推广   总被引:1,自引:0,他引:1  
吕中学  谢鸿政 《数学进展》2003,32(4):419-424
本文通过引入一些常数,运用一些分析技巧和Young不等式,给出了Hilbert积分不等式的一些新的改进和推广。  相似文献   

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