G. Allain

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math.AP2013

Uniqueness of positive periodic solutions with some peaks

Geneviève Allain, Anne Beaulieu

This work deals with the semi linear equation $- Δ u + u - u^{p} = 0$ in $R^{N}$ , $2 \leq p < \frac{N + 2}{N - 2}$ . We consider the positive solutions which are ${2π\over\ep}$-periodic in $x_{1}$ and d…

math.AP2011

An a priori estimate for a singly periodic solution of a semilinear equation

Geneviève Allain, Anne Beaulieu

There exists an exponentially decreasing function $f$ such that any singly $2 π$ -periodic positive solution $u$ of $- Δ u + u - u^{p} = 0$ in $[0, 2 π] \times R^{N - 1}$ verifies $u(x_1,x')\leq…