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1.
二阶非线性椭圆型方程于无界域上的斜微商问题   总被引:1,自引:1,他引:0       下载免费PDF全文
在机械和物理中有许多问题的数学模型是一、二阶非线性椭圆型方程于包含无穷远点的多连通域上的某些边值问题,该文讨论了二阶非线性椭圆型方程于包含无穷远点的多连通域上的斜微商边值问题.  相似文献   

2.
本文讨论平面多连通区域上一般的二阶线性一致椭圆型方程带位移的复合边值问题F.首先,我们提出一阶线性椭圆型复方程的一种变态边值问题G,并给出在某些条件下的问题G解的先验估计式。然后,使用上述结果与线性算子方程的Fredholm定理,可得关于边值问题G与问题F的可解性定理。上述边值问题包含多连通区域上的Poincaré边值问题作为特殊情形。  相似文献   

3.
闻国椿 《数学学报》1983,26(5):533-537
<正> 在L.Bers和L.Nirenberg的文[1]中,研究了一定条件下的二阶非线性一致椭圆型方程 Φ(x,y,u,u_x,u_y,u_(xx),u_(xy),u_(yy))=0(1.1)于单连通区域上的Dirichlet边值问题与Neumann边值问题解的存在性.近几年来,我们也曾对二阶非线性一致椭圓型方程的复形式讨论过解的一些性质与平面多连通区域D上的第一、二、三边值问题与混合边值问题的可  相似文献   

4.
主要讨论求解一类二阶非线性一致椭圆型方程在多连通无界区域上非正则斜微商问题的近似方法.如果此方程和边界条件满足一定的条件,可以得到此边值问题的可解性结果.但是先要使用反证法,求得变态边值问题解的估计式,进而使用解的估计和连续性方法,得到变态边值问题的近似解,最后近似解的误差估计也可给出.  相似文献   

5.
闻国椿 《中国科学A辑》1982,25(9):771-780
本文主要讨论二阶非线性一致椭圆型方程组在多连通区域上斜微商边值问题的可解性。文中提出了一类一阶微分积分方程组的变态Riemann-Hilbert边值问题,建立了这种变态问题解的积分表示式与先验估计式,进而用Leray-Schauder定理证明了此边值问题解的存在性,然后便可导出满足某些条件下的二阶非线性方程组原斜微商问题的可解性结果。  相似文献   

6.
本文主要讨论带有无界可测系数的二阶非线性椭圆型复方程组于多连通区域上的混合边值问题。先给出解的先验估计,引进 Banach 空间,化成积分方程组问题,然后利用Leray—Schauder 不动点定理证明了解的存在定理。本文的最后,还讨论了更一般形式的混合边值问题的可解性。  相似文献   

7.
§1 引言本文中,我们考虑单连通区域D上的二阶非线性一致椭圆型方程:  相似文献   

8.
本文讨论了一阶非线性椭圆型复方程组于平面多连通区域上的一类复合边值问题解的先验估计及可解性.  相似文献   

9.
研究了一类二阶非线性差分方程两点边值问题解的多重性.当该问题的非线性项在无穷远点具有特殊的渐近线性性质时,利用变分方法,结合临界群与Morse理论,同时考虑正、负能量泛函的临界点,不论该问题是否发生共振,均证明了它至少存在两个非零解.  相似文献   

10.
本文中,我们讨论二阶非线性一致椭圆型方程组(1.1)在多连通区域上的第三边值问题(问题Ⅲ)。首先,我们证明了调和函数问题Ⅲ解的存在唯一性,并建立了方程组(1.1)问题Ⅲ解的积分表示。然后,使用上述结果,方程组(1.1)问题Ⅲ解的先验估计以及Leray-Schauder定理,我们得到了满足某些条件的二阶非线性椭圆型方程组(1.1)问题Ⅲ的可解性结果。  相似文献   

11.
1 IntroductionDifferent kinds of numerical n1etl1ods llavc been apPlied to so1lle proble1l1s o11 exteriordolllai11s successf1lly, e.g. tlle bou11dary element metl1od, the absorbillg boundary condi-tion lnethod, the spectrunl 11letllod, a11d the i11fillite eleIue1lt 1nethod. Tlle il1finite elementllletllod llas beell applied to tl1e Laplace equatioll['], the Stokes equation[']['], the plane elastic-ity systeln['1, alld the Heln1ho1tz equatioll[n. We study tl1e infinite ele111ent llletl1od tbr…  相似文献   

12.
In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain. For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincare boundary value problem.  相似文献   

13.
This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.  相似文献   

14.
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The uniqueness theorem of solutions for the above problems and somea priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding theorems in literature. Project supported by the National Natural Science Foundation of China (Grant No. 19671006).  相似文献   

15.
Summary Types of boundary value problems of partial differential equations for infinite domains are discussed which can easily be transformed in such a manner as to allow estimations of error (for approximate solutions) similar to the boundary maximum principle. First, second und third boundary value problems for the outer domain of linear elliptic and certain linear and nonlinear parabolic differential equations are examined. For elliptic differential equations one of the results is that the secound boundary value problem for more than two dimensions can be included. The estimates of the paper can thus be applied to problems of flow around some object, not in the case of two but of three dimensions. This is in a certain sense a counterpart to the conformal mappings method which is successful for two but not for three dimensions. Numerical examples show that estimations of error can easily be carried out.  相似文献   

16.
In this paper, the unique solvability of oblique derivative boundary value problems for second order nonlinear equations of mixed (elliptic-hyperbolic) type in multiply connected domains is proved, which mainly is based on the representation of solutions for the above boundary value problem, and the uniqueness and existence of solutions of the above problem for the equation uxx + sgn y uyy = 0.  相似文献   

17.
In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.  相似文献   

18.
In this paper we find conditions that guarantee that regular boundary value problems for elliptic differential-operator equations of the second order in an interval are coercive and Fredholm, and we prove the compactness of a resolvent. We apply this result to find some algebraic conditions that guarantee that regular boundary value problems for degenerate elliptic differential equations of the second order in cylindrical domains have the same properties. Note that considered boundary value conditions are nonlocal and are differential only in their principal part, and a domain is nonsmooth.  相似文献   

19.
This paper deals with some general irregular oblique derivative problems for nonlinear uniformly elliptic equations of second order in a multiply connected plane domain. Firstly, we state the well-posedness of a new set of modified boundary conditions. Secondly, we verify the existence of solutions of the modified boundary-value problem for harmonic functions, and then prove the solvability of the modified problem for nonlinear elliptic equations, which includes the original boundary-value problem (i.e. boundary conditions without involving undertermined functions data). Here, mainly, the location of the zeros of analytic functions, a priori estimates for solutions and the continuity method are used in deriving all these results. Furthermore, the present approach and setting seems to be new and different from what has been employed before.The research was partially supported by a UPGC Grant of Hong Kong.  相似文献   

20.
In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.  相似文献   

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