Ignacio Guerra

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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…