Results 1 to 10 of about 2,542,949 (203)

Existence and nonexistence of entire solutions for non-cooperative cubic elliptic systems [PDF]

, 2010
In this paper we deal with the cubic Schr\"odinger system $ -\Delta u_i = \sum_{j=1}^n \beta_{ij}u_j^2 u_i$, $u_1,\dots,u_n \geq 0$ in $\mathbb{R}^N (N\leq 3)$, where $\beta=(\beta_{i,j})_{ij}$ is a symmetric matrix with real coefficients and $\beta_{ii}\
Tavares, Hugo, Terracini, Susanna, Verzini, Gianmaria, Weth, Tobias   +3 more
core   +3 more sources

Entire large solutions for semilinear elliptic equations [PDF]

, 2012
We analyze the semilinear elliptic equation $\Delta u=\rho(x) f(u)$, $u>0$ in ${\mathbf R}^D$ $(D\ge3)$, with a particular emphasis put on the qualitative study of entire large solutions, that is, solutions $u$ such that $\lim_{|x|\rightarrow +\infty}u(x)
Bidaut-Veron, Brezis, Cheng, Cheng, Costin, Dumont, Dupaigne, Dynkin, Engländer, Gidas, Gilbarg, Guillaume Warnault, Hebey, Keller, Lair, Le Gall, Li, Li, Louis Dupaigne, Marius Ghergu, Ni, Olivier Goubet, Olofsson, Osserman, Ren, Schaefer, Taliaferro, Taliaferro, Yamabe, Ye, Ye   +30 more
core   +3 more sources

Entire solutions of hydrodynamical equations with exponential dissipation [PDF]

, 2009
We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose ...
A. Doelman, A. Ferrari, C. Cao, C. Foias, C.M. Cox, C.R. Doering, Claude Bardos, D. Gottlieb, D. Li, D. Senouf, Edriss S. Titi, G. Holloway, H. Sohr, J. Hoeven van der, J.L. Lions, K. Masuda, M. Oliver, M.-E. Brachet, O.A. Ladyzhenskaya, P. Constantin, R.E. Caflisch, R.H. Kraichnan, Samriddhi Sankar Ray, U. Frisch, U. Frisch, U. Frisch, U. Frisch, Uriel Frisch, W. Pauls, W. Pauls, Walter Pauls, Ya.G. Sinai   +31 more
core   +6 more sources

Negatively Invariant Sets and Entire Solutions [PDF]

, 2010
Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated in terms of processes, are shown to contain a strictly invariant set and hence entire solutions.
Kloeden, Peter E., Marín Rubio, Pedro
core   +1 more source

Nonradial entire solutions for Liouville systems

, 2017
We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-\Delta u_1=2e^{u_1}+\mu e^{u_2}&\text{in }\mathbb R^2\\-\Delta u_2=\mu e^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\int_{\mathbb R^2}e^{u_1}
Battaglia, Luca, Gladiali, Francesca, Grossi, Massimo   +2 more
core   +1 more source

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
core   +1 more source

Entire solutions of sublinear elliptic equations in anisotropic media

, 2005
We study the nonlinear elliptic problem $-\Delta u=\rho (x)f(u)$ in $\RR^N$ ($N\geq 3$), $\lim\_{|x|\ri\infty}u(x)=\ell$, where $\ell\geq 0$ is a real number, $\rho(x)$ is a nonnegative potential belonging to a certain Kato class, and $f(u)$ has a ...
Dinu, Teodora Liliana
core   +1 more source

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
core   +1 more source

Entire solutions with exponential growth for an elliptic system modeling phase-separation

, 2013
We prove the existence of entire solutions with exponential growth for the semilinear elliptic system [\begin{cases} -\Delta u = -u v^2 & \text{in $\R^N$} -\Delta v= -u^2 v & \text{in $\R^N$} u,v>0, \end{cases}] for every $N \ge 2$.
Soave, Nicola, Zilio, Alessandro
core   +1 more source

Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

, 2009
In this paper, we study the following degenerate critical elliptic equations with anisotropic coefficients $$ -div(|x_{N}|^{2\alpha}\nabla u)=K(x)|x_{N}|^{\alpha\cdot 2^{*}(s)-s}|u|^{2^{*}(s)-2}u {in} \mathbb{R}^{N} $$ where $x=(x_{1},...,x_{N})\in ...
B. Franchi, B. Gidas, C. P. Wang, D. Castorina, D. Gilbarg, D. M. Cao, G. H. Hardy, G. Mancini, G. Mancini, H. Egnell, J. D. Fernandes, J. Serrin, LiShan Lin, M. Gazzini, R. Monti, S. W. Chen, ShaoWei Chen, V. G. Maz’ya, Y. Y. Li, Y. Y. Li, Y. Y. Li   +20 more
core   +1 more source