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math.AP2011
The Gardner equation and the stability of multi-kink solutions of the mKdV equation
Claudio Muñoz
Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse are shown to be globally -stable. Stability in the one-kink case was previou…
math.AP2011★ 8 cited
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation
Miguel A. Alejo, Claudio Muñoz, Luis Vega
Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingl…
math.AP2006
The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity
Manuel del Pino, Claudio Muñoz
We consider the problem of Ambrosetti-Prodi type \begin{equation}\label{0}\quad\begin{cases} Δu + e^u = sϕ_1 + h(x) &\hbox{in} Ω, u=0 & \hbox{on} \partial Ω, \end{cases} \nonumber…