首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 78 毫秒
1.
一类新的弱奇性Volterra 积分不等式解的估计   总被引:3,自引:1,他引:2  
收稿研究了一类新的含有多个非线性项的弱奇性Volterra积分不等式解的估计,所得结果推广了过去关于弱奇性Volterra型积分不等式的相关结果,并用实例给出了解的估计.  相似文献   

2.
刘兴燕  曾德宇 《大学数学》2015,31(2):108-113
建立了一类有两个变量的非线性弱奇性Wendroff型积分不等式解的估计,所得结果推广了过去关于非线性弱奇性Wendroff型积分不等式的相关结果,所给出的解的估计更具有一般性.  相似文献   

3.
在参数更广的分布下,讨论了一类新的弱奇性Wendroff型积分不等式解的估计,所得结果推广了已有的相关结果,并将结果应用到研究微分方程解的有界性中.  相似文献   

4.
在参数α,β,γ更广的分布下,给出了一类弱奇性Wendroff型积分不等式解的有限形式的界公式,所得结果推广了过去关于弱奇性Wendroff型积分不等式的相关结果,并将结果应用到微分方程中.  相似文献   

5.
奇摄动Volterra型积分微分方程Robin问题   总被引:11,自引:0,他引:11  
张祥 《数学季刊》1992,7(3):24-31
本文利用上、下解证明了Volterra型积分微分方程解的存在性。然后,应用所获得的微分不等式理论,在适当的假设下,通过构造特殊的上、下解函数,证明Volterra型 奇摄动积分微分方程解的存在性,并给出一致有效的解的渐近估计。  相似文献   

6.
在参数更广的分布下,讨论了一类含有两项非线性项的弱奇性Wendroff型积分不等式解的估计,所得结果推广了在相应参数不同的分布下已有的相关结果且结果更简洁、更具一般性,并将结果应用到研究微分方程解的有界性中.  相似文献   

7.
陈丽华 《数学研究》1998,31(3):302-307
研究含多个Volterra型积分算子的积分微分方程组Robin边值问题的奇摄动.在适当的条件下,利用微分不等式理论,证明了解的存在及解的按分量一致有效的估计.  相似文献   

8.
一个推广的二变量时滞积分不等式及其应用   总被引:1,自引:1,他引:0  
建立了一类二变量的时滞积分不等式,不等式包含一个一重积分和两个二重积分,二重积分内包含两个不同的没有假设单调性的未知函数的复合函数.使用单调化技术,给出积分不等式中未知函数的估计.结果能对相关文献中考虑的积分不等式中未知函数进行估计.进一步,结果给出了一类积分-微分方程解的估计.  相似文献   

9.
Volterra型积分微分方程非线性边值问题   总被引:10,自引:0,他引:10  
本文首先利用上、下解方法研究了一类Volterta型积分微分方程Dirichlet问题和非线性边值问题的解的存在性;然后,利用所得到的微分不等式理论考虑一类相应的奇摄动非线性边值问题,获得包括边界层在内的一致有效渐近解的存在性。  相似文献   

10.
通过Poisson积分构造向量核函数,利用向量情形的奇弄积分算子的强型估计与弱型估计理论,建立了k阶Stein函数的强型估计、弱型估计与BMO模估计,完全解决了A阶Stein函数的有界性问题。  相似文献   

11.
Bounds on solutions to a new class of nonlinear integral inequalities with weakly singular kernels are established by the de-singularity approach.  相似文献   

12.
Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. Some applications to fractional differential and integral equations are also indicated.  相似文献   

13.
By studying a weakly singular integral whose kernel involves Mittag-Leffler functions, we obtain some new Gronwall-type integral inequalities. Applying these inequalities and fixed point theorems, existence and uniqueness of positive solution of initial value problem to nonlinear fractional differential equation with Caputo-like counterpart hyper-Bessel operators are established.  相似文献   

14.
In this paper, a Schauder decomposition in Lp is used to obtain numerical solutions for the Fredholm integral equations of the second kind. Considerations are also given to weakly singular integral equations and two dimensional weakly singular integral equations.  相似文献   

15.
Three iterative refinement schemes are studied for approximating the solutions of linear weakly singular Fredholm integral equations of the second kind. The rates of convergence and computational costs of the three schemes are studied and compared with the classical approach by applying them respectively to: (i) a sparse linear system associated with an integral equation modelling a real life Astrophysics problem, and (ii) an integral equation whose associated linear problem is dense.  相似文献   

16.
Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial collocation methods on graded grids for nonlinear Volterra integral equations with algebraic or logarithmic singularities in their kernels.

  相似文献   


17.
Sheng Chen 《数学研究》2020,53(2):143-158
Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods.  相似文献   

18.
In this article, our main goal is to render an idea to convert a nonlinear weakly singular Volterra integral equation to a non‐singular one by new fractional‐order Legendre functions. The fractional‐order Legendre functions are generated by change of variable on well‐known shifted Legendre polynomials. We consider a general form of singular Volterra integral equation of the second kind. Then the fractional Legendre–Gauss–Lobatto quadratures formula eliminates the singularity of the kernel of the integral equation. Finally, the Legendre pseudospectral method reduces the solution of this problem to the solution of a system of algebraic equations. This method also can be utilized on fractional differential equations as well. The comparison of results of the presented method and other numerical solutions shows the efficiency and accuracy of this method. Also, the obtained maximum error between the results and exact solutions shows that using the present method leads to accurate results and fast convergence for solving nonlinear weakly singular Volterra integral equations. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
We propose iterated fast multiscale Galerkin methods for the second kind Fredholm integral equations with mildly weakly singular kernel by combining the advantages of fast methods and iteration post-processing methods. To study the super-convergence of these methods, we develop a theoretical framework for iterated fast multiscale schemes, and apply the scheme to integral equations with weakly singular kernels. We show theoretically that even the computational complexity is almost optimal, our schemes improve the accuracy of numerical solutions greatly, and exhibit the global super-convergence. Numerical examples are presented to illustrate the theoretical results and the efficiency of the methods.  相似文献   

20.
Generalized solutions of weakly coupled functional differential systems are investigated. Theorems on the existence, uniqueness and continuous dependence upon initial data are given. The local Cauchy problem is transformed into functional integral equations. The method of bicharacteristics and integral inequalities are used.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号