共查询到20条相似文献,搜索用时 187 毫秒
1.
1.APrioriBounds##DTherearealotofresultsfortheprioriboundsandtheexistenceofpositivesolutionsofsemilinearellipticequations(see[2],[3]).Weshallinvestigatetheprioriboundsandtheexistenceofpositivesolutionsforsystemofellipticboundaryvalueproblems:Wealwaysassume… 相似文献
2.
Harnack type inequalities for nonnegative (weak) solutions of degenerate elliptic equations, in divergence form, are established. The asymptotic behavior of solutions of Fuchsian type weighted elliptic operators is also investigated. 相似文献
3.
鲁又文 《纯粹数学与应用数学》1994,(2)
设Ω为En中的无界,连通区域.在Ω×(0,∞)上考虑抛物型方程:设,B满足结构条件:设存在和,使对任何ρ0>ρ1>0:设u是方程的广义解,并且如果u在Ω×(0,T)为有界,那么u+≤0. 相似文献
4.
SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS 总被引:1,自引:0,他引:1
Tie Zhang 《计算数学(英文版)》2002,(3)
AbstractSome superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively. 相似文献
5.
We obtain selfgravitating multi-string configurations for the Einstein-Weinberg-Salam model, in terms of solutions for a nonlinear elliptic system of Liouville type whose solvability was posed as an open problem in Yang (Solitons in Field Theory and Nonlinear Analysis, Springer, New York, 2001). 相似文献
6.
套格图桑 《高校应用数学学报(A辑)》2017,32(1)
给出函数变换,变量分离形式解与第一种椭圆方程相结合的方法,构造了(2+1)维modified Zakharov-Kuznetsov(m ZK)方程的多种复合型新解.步骤一,给出两种函数变换,将(2+1)维m ZK方程转化为能够获得变量分离解的非线性发展方程.步骤二,给出非线性发展方程的变量分离形式解,通过第一种椭圆方程及其相关结论,构造了(2+1)维m ZK方程的双孤子解和双周期解等复合型新解. 相似文献
7.
《Applied Mathematics Letters》2003,16(2):243-248
We show the existence and nonexistence of positive solutions for a transmission problem given by a system of two nonlinear elliptic equations of Kirchhoff type. 相似文献
8.
9.
利用新近提出的F展开法,导出了Davey StewartsonⅠ方程的由Jacobi椭圆函数表示的周期波解;并且在极限的情况下,得到了Davey StewartsonⅠ方程的孤波解以及其他形式解. 相似文献
10.
Mouhamed Moustapha Fall 《偏微分方程通讯》2013,38(2):354-397
Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the singularity of solutions to linear and semilinear fractional elliptic equations with a homogeneous singular potential related to the fractional Hardy inequality. As a consequence we obtain unique continuation properties for fractional elliptic equations. 相似文献
11.
Nihed TRABELSI 《数学物理学报(B辑英文版)》2018,38(4):1174-1194
The existence of singular limit solutions are investigated by establishing a new Liouville type theorem for nonlinear elliptic system with sub-quadratic convection term and by using the nonlinear domain decomposition method. 相似文献
12.
A. A. Akhmetshin I. M. Krichever Yu. S. Volvovski 《Functional Analysis and Its Applications》2002,36(4):253-266
We present a Lax pair for the field elliptic Calogero-Moser system and establish a connection between this system and the Kadomtsev-Petviashvili equation. Namely, we consider elliptic families of solutions of the KP equation such that their poles satisfy a constraint of being balanced. We show that the dynamics of these poles is described by a reduction of the field elliptic CM system.We construct a wide class of solutions to the field elliptic CM system by showing that any N-fold branched cover of an elliptic curve gives rise to an elliptic family of solutions of the KP equation with balanced poles. 相似文献
13.
LIU Chungen 《数学年刊B辑(英文版)》2000,21(2):225-232
51.IntroductionandMainResultsInthispaper,weconsiderthestabilityoftheperiodicsolutionsofthefollowingsecondorderHamiltoniansystemswherenisapositiveillteger.V:Rxac-RisafUnctionandforT>0itisT-periodicforthevariablet.VJdenotesitsgradientwithrespecttox.Wenowstatethemainresultsofthispaper.Forthesuperquadraticcase)wehavethefollowingtwotheoremsTheorem1.1.SmposeVsatiSfiesthefollowingconditions:(VI)VEC'(RxR",R)andV(t T,x)=V(t,x),V(t,x)ERxR".(V2)ThereexistconstantSp>2andco>0suchthat0相似文献
14.
In this paper, we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part. Firstly, we study the qualitative properties, such as the symmetry, regularity and asymptotic behavior of the positive solutions. Secondly, we classify the non-positive solutions by proving some Liouville type theorems for the finite Morse index solutions and stable solutions to the nonlocal elliptic equations with double weights.
相似文献15.
《数学物理学报(B辑英文版)》2020,(4)
In this article, we study the blow-up solutions for a case of b-family equations.Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution. 相似文献
16.
The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities.It is shown,by means of variational methods,that under certain conditions,the system has at least two positive solutions. 相似文献
17.
Sami Baraket 《复变函数与椭圆型方程》2018,63(1):37-67
We study the existence of singular limit solutions for a nonlinear elliptic system of Liouville type with a singular source term given by Dirac masses and Dirichlet boundary conditions. We use the nonlinear domain decomposition method. 相似文献
18.
We construct integrable pseudopotentials with an arbitrary number of fields in terms of an elliptic generalization of hypergeometric
functions in several variables. These pseudopotentials are multiparameter deformations of ones constructed by Krichever in
studying the Whitham-averaged solutions of the KP equation and yield new integrable (2+1)-dimensional systems of hydrodynamic type. Moreover, an interesting class of integrable (1+1)-dimensional systems described in terms of solutions of an elliptic generalization of the Gibbons-Tsarev system is related
to these pseudopotentials. 相似文献
19.
《Applied Mathematics Letters》2003,16(4):581-587
The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems. 相似文献
20.
一类非牛顿渗流系统爆破界的估计 总被引:4,自引:1,他引:3
首先得到一类拟线性椭圆型方程组的正解的先验界估计和衰减性质,从而推出该方程组的径向非增正对称解的不存在性结果.利用此结果建立了一类拟线性反应扩散方程组(非牛顿渗流系统)的爆破界的估计,推广了半线性(Fujita型)反应扩散方程组的结果. 相似文献