Results 41 to 50 of about 2,542,949 (203)

A Bernstein result and counterexample for entire solutions to Donaldson's equation [PDF]

arXiv, 2015
We show that convex entire solutions to Donaldson's equation are quadratic, using a result of Weiyong He. We also exhibit entire solutions to the Donaldson equation that are not of the form discussed by He. In the process we discover some non-trivial entire solutions to complex Monge-Amp\`{e}re equations.
arxiv  

On the confinement of bounded entire solutions to a class of semilinear elliptic systems [PDF]

, 2014
Under appropriate assumptions, we show that all bounded entire solutions to a class of semilinear elliptic systems are confined in a convex domain. Moreover, we prove a Liouville type theorem in the case where the domain is strictly convex.
Sourdis, Christos
core   +1 more source

Entire solutions of semilinear elliptic equations

Electronic Journal of Differential Equations, 2004
We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors.
Alexander Gladkov, Nickolai Slepchenkov
doaj  

Ordinary differential equations with only entire solutions [PDF]

arXiv, 1997
We prove necessary and sufficient conditions for a system $\dot z_i=z_ip_i(z)$ ($p_i$ a polynomial) to have only entire analytic functions as solutions.
arxiv  

Entire Solutions of the Fisher-KPP Equation on the Half Line [PDF]

arXiv, 2018
In this paper we study the entire solutions of the Fisher-KPP equation $u_t=u_{xx}+f(u)$ on the half line $[0,\infty)$ with Dirichlet boundary condition at $x=0$. (1). For any $c\geq 2\sqrt{f'(0)}$, we show the existence of an entire solution $\mathcal{U}^c(x,t)$ which connects the traveling wave solution $\phi^c(x+ct)$ at $t=-\infty$ and the unique ...
arxiv  

Entire Solutions of Diffusive Lotka-Volterra System [PDF]

arXiv, 2020
This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system \begin{equation}\label{eq:abstract} \begin{cases} u_{t}= u_{xx} + u(1-u-av), & \qquad \ x\in\mathbb{R} \cr v_{t}= d v_{xx}+ rv(1-v-bu), & \qquad \ x\in\mathbb{R} \end{cases} \quad (1) \end{equation} where $d,r,a$, and $b$ are positive ...
arxiv  

Entire Solutions Of Certain Non-Linear Differential-Difference Equations [PDF]

arXiv, 2021
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
arxiv  

Fermat type differential and difference equations

Electronic Journal of Differential Equations, 2015
This article we explore the relationship between the number of differential and difference operators with the existence of meromorphic solutions of Fermat type differential and difference equations. Some Fermat differential and difference equations of
Kai Liu, Xianjing Dong
doaj  

Existence of entire solutions for semilinear elliptic systems under the Keller-Osserman condition

Electronic Journal of Differential Equations, 2011
Under the Keller-Osserman condition on $f+g$, we show the existence and nonexistence of entire solutions for the semilinear elliptic system $Delta u =p(x)f(v), quad Delta v =q(x)g(u),quad xin mathbb{R}^N$, where $p,q:mathbb{R}^No [0,infty)$ are ...
Zhijun Zhang, Yongxiu Shi, Yanxing Xue
doaj  

Entire Solutions for the Classical Competitive Lotka-Volterra System with Diffusion in the Weak Competition Case [PDF]

arXiv, 2017
In this paper we are concerned with the entire solutions for the classical competitive Lotka-Volterra system with diffusion in the weak competition. For this purpose we firstly analyze the asymptotic behavior of traveling front solutions for this system connecting the origin and the positive equilibrium.
arxiv