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 $2\pi$-periodic positive solution $u$ of $-\Delta u+u-u^p=0$ in $[0,2\pi ]\times {\mathbb{R}}^{N-1}$ verifies $u(x_1,x')\leq…