Results 11 to 20 of about 10,090,746 (128)
Multidimensional entire solutions for an elliptic system modelling phase separation
, 2016 For the system of semilinear elliptic equations \[ \Delta V_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in $\mathbb{R}^N$} \] we devise a new method to construct entire solutions.
Soave, Nicola, Zilio, Alessandro
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Entire solutions of quasilinear elliptic systems on Carnot Groups
, 2013 We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems.
D'Ambrosio, Lorenzo, Mitidieri, Enzo
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Closed-Flux Solutions to the Constraints for Plane Gravity Waves
, 1996 The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar.
A. Ashtekar +10 more
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Generalized Harnack inequality for semilinear elliptic equations
, 2016 This paper is concerned with semilinear equations in divergence form \[ \diver(A(x)Du) = f(u) \] where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical
Julin, Vesa
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Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation
, 2019 The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u = u-u^3-\delta$ in $\R^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder.
Rizzi, Matteo
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Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in $\Er^2$
, 2011 In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane.
A. Bonnet +41 more
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Nevanlinna Theory for Jackson Difference Operators and Entire Solutions of q-Difference Equations [PDF]
Analysis Mathematica, 2018 This paper has two purposes. One is to establish a version of Nevanlinna theory based on the historic so-called Jackson difference operator Dqf(z)=f(qz)−f(z)qz−z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}
T. Cao, H. Dai, J. Wang
semanticscholar +1 more source
Entire solutions in nonlocal monostable equations: Asymmetric case
Communications on Pure and Applied Analysis, 2019 This paper is concerned with entire solutions of the monostable equation with nonlocal dispersal, i.e., \begin{document}$u_{t}=J*u-u+f(u)$\end{document} . Here the kernel \begin{document}$J$\end{document} is asymmetric.
Yu-Juan Sun +3 more
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Entire solutions to semilinear nonlocal equations in $\RR^2$
, 2015 We consider entire solutions to $L u= f(u)$ in $\RR^2$, where $L$ is a general nonlocal operator with kernel $K(y)$. Under certain natural assumtions on the operator $L$, we show that any stable solution is a 1D solution.
Ros-Oton, Xavier, Sire, Yannick
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Entire solutions and traveling wave solutions of the Allen-Cahn-Nagumo equation
Discrete and Continuous Dynamical Systems. Series A, 2019 In this paper, the propagation phenomena in the Allen-Cahn-Nagumo equation are considered. Especially, the relation between traveling wave solutions and entire solutions is discussed.
H. Ninomiya
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