Université de Picardie Jules Verne

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math.AP2009★ 6 cited

Global attractor for weakly damped Nonlinear Schrödinger equations in $L^{2} (R)$

Olivier Goubet, Luc Molinet

We prove that the weakly damped nonlinear Schrödinger flow in $L^{2} (R)$ provides a dynamical system which possesses a global attractor. The proof relies on the continuity o…

math.AP2008★ 3 cited

Stable solutions of elliptic equations on Riemannian manifolds

Alberto Farina, Yannick Sire, Enrico Valdinoci

This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. A…

math.AP2008

Stable solutions for the bilaplacian with exponential nonlinearity

Juan Davila, Louis Dupaigne, Ignacio Guerra +1

Let $λ^{*} > 0$ denote the largest possible value of $λ$ such that \begin{align*} \left\{\begin{aligned} Δ^2 u & = \la e^u && \text{in $B$ } u &= \pd{u}{n} = 0 && \text{on $ \pa B $} \…

math.AP2008

Perturbing singular solutions of the Gelfand problem

Juan Davila, Louis Dupaigne, Ignacio Guerra +1

he equation $- Δ u = λ e^{u}$ posed in the unit ball $B \subseteq R^{N}$ , with homogeneous Dirichlet condition $u ∣_{\partial B} = 0$ , has the singular solution $U = lo g \frac{1}{∣ x ∣ ^{2}}$ when…

Global attractor for weakly damped Nonlinear Schrödinger equations in L2(R)

Stable solutions of elliptic equations on Riemannian manifolds

Stable solutions for the bilaplacian with exponential nonlinearity

Perturbing singular solutions of the Gelfand problem

Global attractor for weakly damped Nonlinear Schrödinger equations in $L^{2} (R)$