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1.
应用Green函数将分数阶微分方程边值问题可转化为等价的积分方程.近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性.本文讨论奇异非线性分数阶微分方程边值问题正解的唯一性.应用Green函数将其转化为等价的积分方程,利用偏序集上的不动点定理证明正解的唯一性. 相似文献
2.
分数阶微分方程耦合系统边值问题解的存在性 总被引:4,自引:0,他引:4
应用Green函数将微分方程边值问题可转化为等价的积分方程.近来此方法被应用于讨论分数阶微分方程边值问题正解的存在性.本文讨论非线性分数阶微分方程耦合系统的两点边值问题,应用Green函数,将其转化为等价的积分方程耦合系统,并设非线性项在无穷远处有增长条件,应用Schauder不动点定理证明解而非限于正解的存在性. 相似文献
3.
应用Green函数可以将微分方程边值问题转化为等价的积分方程.近来此方法被应用于讨论微分方程边值问题正解的存在性.本文讨论非线性二阶Neumann边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项在无穷远处有增长条件,利用锥上的不动点指数理论证明正解的存在性和非存在性. 相似文献
4.
应用Green函数将分数阶微分方程边值问题可转化为等价的积分方程.近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性.本文讨论非线性分数阶微分方程边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项满足Carathéodory条件,利用非紧性测度的性质和M(o)nch,s不动点定理证明解的存在... 相似文献
5.
利用Green函数可以将分数阶微分方程初值问题转化为等价的积分方程.近来此方法被应用于讨论非线性分数阶微分方程初值问题解的存在性.本文讨论菲线性分数阶脉冲微分方程初值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项满足Carathéodory条件,利用非紧性测度的性质和M(o)nch,8不动点定理证明解的存在性. 相似文献
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7.
一类Hammerstein型积分方程及其应用 总被引:3,自引:0,他引:3
在不假定核函数非负的条件下,利用锥与半序方法及不动点指数理论,结合线性算子的谱半径,讨论了非线性Hammerstein型积分方程非零解的存在性。并将所得抽象结果具体应用于常微分方程两点边值问题,得到了上列积分方程存在非零解的新结论。 相似文献
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9.
一类泛函微分方程边值问题的多重正解 总被引:1,自引:1,他引:0
本文讨论了一类二阶泛函微分方程边值问题。首先将此问题转化为分段的积分方程,然后利用锥上的不动点定理讨论了其多重正解的存在性,得到了此二阶泛函微分方程存在两个正解的结果。 相似文献
10.
随机微分方程广泛地出现于经济学、生物学、物理学、电子、无线电通讯等领域,所以研究随机微分方程的解是十分必要的。由于随机微分方程的解析解求解困难,其数值方法的研究越来越引起人们的重视。对于求解随机微分方程的数值方法,衡量其有效性的标准是收敛性和稳定性。本文证明混合欧拉格式用于求解自治标量随机微分方程时,在方程的偏移系数和扩散系数均满足线性增长条件和全局Lipschitz条件时的收敛性,并且求出了局部均值收敛阶和均方强收敛阶。接着讨论了两种试验方程混合欧拉格式的稳定性。 相似文献
11.
《International Journal of Engineering Science》2002,40(18):2023-2040
The problems dealing with some simple unsteady unidirectional flows of a mixture of two incompressible Newtonian fluids are investigated. By using the constitutive equations appeared in the literature for binary mixtures of chemically inert incompressible Newtonian fluids, the equations governing the motion of the binary mixture are reduced to a system of coupled partial differential equations. By means of integral transforms, the exact solutions of these equations are obtained for the following three problems: (i) unsteady Couette flow, (ii) unsteady plane Poiseuille flow, (iii) unsteady axisymmetric Poiseuille flow. 相似文献
12.
F. M. E. Duddeck 《Computational Mechanics》2008,41(6):749-757
The range of applications of Boundary Element Methods (BEM) is restricted to cases where the fundamental solution is known.
An approach recently developed by the author via the Fourier transform generalizes the BEM to the so-called Fourier BEM (Fourier
BEM—generalization of boundary element methods by Fourier Transform. Springer, Berlin Heidelberg New York, 2002). There, new
boundary integral equations (BIE) are formulated, which consist only of Fourier transformed terms and lead to equivalent matrices
as in the standard approach. They make use of only the Fourier transform of the fundamental solution, which is much easier
to obtain (available for all cases as long as the differential operator is linear and has constant coefficients). No inverse
transform and no fundamental solution in the original space are required. Here, the theory is summarized and an example of
anisotropic elasticity is given to motivate the discussion of singularities, which is the topic of this paper. It is shown,
that all types of singularities (weak, strong, and hyper) occur as in the standard approach and that they require a new treatment
because they are originating from newly developed integral equations. The main result is that the non-regular parts of the
strong and hyper singular integrals cancel if ordered correctly. 相似文献
13.
《Engineering Analysis with Boundary Elements》1999,23(7):603-609
The paper provides a new method for obtaining the fundamental integral representation used in BEM. The method is based on integral transforms and can be applied to all linear differential equations with constant coefficients. Some explicit formulae pertaining to potential problems, linear elasticity and low Reynolds number flows are derived. 相似文献
14.
Associate Prof. Dr. T. Watanabe 《Acta Mechanica》1991,87(1-2):1-9
Summary The effect of uniform suction or injection on free convection boundary layer over a cone was theoretically investigated. The non-linear ordinary differential equations were obtained by the difference-differential method after transforming it to an equivalent two-dimensional problem by Mangler's transformation. The solutions of the resulting equations can be expressed in the form of integral equations. Numerical calculations were performed solving the integral equations by the iterative numerical quadrature. The velocity profiles, temperature profiles, skin friction parameters and heat transfer parameters with constant wall temperature were computed for various values of suction/injection parameter and cone angle parameter. 相似文献
15.
Summary We show formally that integral conversation equations can be related directly to corresponding integral variational statements, without the usual appeal to the classical differential form and the associated smoothness assumptions. 相似文献
16.
S. V. Meleshko S. Moyo C. Muriel J. L. Romero P. Guha A. G. Choudhury 《Journal of Engineering Mathematics》2013,82(1):17-30
Here we discuss first integrals of a particular representation associated with second-order ordinary differential equations. The linearization problem is a particular case of the equivalence problem together with a number of related problems such as defining a class of transformations, finding invariants of these transformations, obtaining the equivalence criteria, and constructing the transformation. The relationship between the integral form, the associated equations, equivalence transformations, and some examples are considered as part of the discussion illustrating some important aspects and properties. 相似文献
17.
Nikola Hajdin Dusan Krajcinovic 《International journal for numerical methods in engineering》1972,4(4):509-522
This paper presents a method of numerical solution of boundary value problems governed by a set of ordinary differential equations. The highest derivative is chosen as the unknown function. Governing equations are transformed into a set of integral equations. The kernels of integral equations turn out to be influence functions for deflection and/or bending moments of a corresponding beam, and can, therefore, be computed using well-known methods of structural analysis. Finally, the unknown function (highest derivative) is approximated in a defined manner and the solution is obtained through numerical integration. 相似文献
18.
U. Heise 《Computational Mechanics》1991,7(5-6):311-328
Fundamental solutions of the operator of Navier's differential equation (equilibrium equation) for the elastostatic boundary value problem are established. The solutions are not defined on the ordinary three-dimensional space as the classical Kelvin solution but on Riemann spaces. They can be used as kernels of boundary integral equations. It should be possible to apply integral equations of this type advantageously for the determination of the state of deformation in elastic bodies parts of the surface of which touch or almost touch each other (bodies with slits, certain helical elastic springs, etc.). 相似文献
19.
Serdar Bar 《International Journal of Engineering Science》2005,43(19-20):1471-1485
This paper is concerned with applying the mixture theory of two chemically inert incompressible Newtonian fluids to some simple unsteady flows in the annular region between two infinitely long coaxial cylinders. The equations governing the motion of the binary mixture under discussion are reduced to a system of coupled partial differential equations. With the help of finite Hankel transforms, the exact solutions of these equations are obtained in series form for the following three problems: (i) unsteady axial Couette flow in an annulus, (ii) unsteady Poiseuille flow in an annulus, (iii) unsteady circular Couette flow in an annulus. 相似文献