Louis Dupaigne

collaborators

3 papers

math.AP2008

Stable solutions of $- Δ u = f (u)$ in $R^{N}$

Louis Dupaigne, Alberto Farina

The paper proves Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearity, posed on the entire Euclidean space. Extensions to solutions whic…

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…

Stable solutions of −Δu=f(u) in RN

Stable solutions for the bilaplacian with exponential nonlinearity

Perturbing singular solutions of the Gelfand problem

Stable solutions of $- Δ u = f (u)$ in $R^{N}$