共查询到20条相似文献,搜索用时 26 毫秒
1.
In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash–Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schrödinger equations with harmonic potential. 相似文献
2.
An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means. 相似文献
3.
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
4.
Guozhen Lu Peiyong Wang Jiuyi Zhu 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2012
Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumptions of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma developed recently in Polá?ik et al. (2007) [20], we improve several Liouville-type theorems in higher order elliptic equations, some semilinear equations and elliptic systems. More specifically, we remove the boundedness assumption of the solutions which is required in the proofs of the corresponding Liouville-type theorems in the recent literature. Moreover, we also investigate the singularity and decay estimates of higher order elliptic equations. 相似文献
5.
Desheng Shang 《Applied mathematics and computation》2010,217(4):1577-1583
In this paper, we employ the general integral method for traveling wave solutions of coupled nonlinear Klein-Gordon equations. Based on the idea of the exact Jacobi elliptic function, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons, periodic solutions and Jacobi elliptic function solutions. 相似文献
6.
In this work, we present a direct new method for constructing the rational Jacobi elliptic solutions for nonlinear differential–difference equations, which may be called the rational Jacobi elliptic function method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential–difference equations in mathematical physics via the lattice equation. The proposed method is more effective and powerful for obtaining the exact solutions for nonlinear differential–difference equations. 相似文献
7.
Meijun Zhu 《Journal of Differential Equations》2003,193(1):180-195
In this paper we prove the existence of positive solutions to some nondivergent elliptic equations with indefinite nonlinear boundary conditions. The proof is based on a new Liouville-type theorem about the nonnegative solutions to some canonical indefinite elliptic equations, which is also proved in this paper by the method of moving planes. 相似文献
8.
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
9.
Minoru Murata 《Journal of Functional Analysis》2002,194(1):53-141
We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations. 相似文献
10.
In this paper, we extend the Jacobi elliptic function rational expansion method by using a new generalized ansätz. With the help of symbolic computation, we construct more new explicit exact solutions of nonlinear evolution equations (NLEEs). We apply this method to a generalized Hirota–Satsuma coupled KdV equations and gain more general solutions. The general solutions not only contain the solutions by the existing Jacobi elliptic function expansion methods but also contain many new solutions. When the modulus of the Jacobi elliptic functions m → 1 or 0, the corresponding solitary wave solutions and triangular functional (singly periodic) solutions are also obtained. 相似文献
11.
Qing Han 《Journal of Geometric Analysis》2000,10(3):455-480
In this paper we first give a priori estimates on asymptotic polynomials of solutions to elliptic equations at nodal points.
This leads to a pointwise version of Schauder estimates. As an application we discuss the structure of nodal sets of solutions
to elliptic equations with nonsmooth coefficients. 相似文献
12.
A Generalized (G'/G)-Expansion Method to Find the Traveling Wave Solutions of Nonlinear Evolution Equations 下载免费PDF全文
In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized (G'/G)-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained. 相似文献
13.
《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
14.
主要利用Jacobi椭圆函数所满足的方程并用其解代替Jacobi椭圆函数以求非线性偏微分方程的周期解,并举例说明该方法的应用. 相似文献
15.
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16.
Guochun Wen 《分析论及其应用》2005,21(2):118-131
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order. 相似文献
17.
In this paper, a variable-coefficient Jacobi elliptic function expansion method is proposed to seek more general exact solutions of nonlinear partial differential equations. Being concise and straightforward, this method is applied to the (2+1)-dimensional Nizhnik-Novikov-Vesselov equations. As a result, many new and more general exact non-travelling wave and coefficient function solutions are obtained including Jacobi elliptic function solutions, soliton-like solutions and trigonometric function solutions. To give more physical insights to the obtained solutions, we present graphically their representative structures by setting the arbitrary functions in the solutions as specific functions. 相似文献
18.
Baojian Hong 《Applied mathematics and computation》2009,215(8):2908-2913
In this work, a new generalized Jacobi elliptic functions expansion method based upon four new Jacobi elliptic functions is described and abundant new Jacobi-like elliptic functions solutions for the variable-coefficient mKdV equation are obtained by using this method, some of these solutions are degenerated to solitary-like solutions and triangular-like functions solutions in the limit cases when the modulus of the Jacobi elliptic functions m→1 or 0, which shows that the new method can be also used to solve other nonlinear partial differential equations in mathematical physics. 相似文献
19.
闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved. 相似文献
20.
Nonnegativity of weak solutions of parabolic and elliptic equations on nonsmooth domains is established. Strong positivity of weak solutions to elliptic equations is proved via a boundary weak Harnack inequality. 相似文献