The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space

Peter Poláčik, Darío A. Valdebenito

We consider the equation ${\Delta }_{x}u+u_{yy}+f(u)=0,x=(x_1,\dots ,x_N)\in {\mathbb{R}}^N,y\in \mathbb{R},$ where $N\ge 2$ and $f$ is a sufficiently smooth function satisfying $f(0)=0$,…