We consider the problem $-\Delta u+F_u(x,u)=0$ on $\R^n$, where $F$ is a smooth function periodic of period 1 in all its variables. We show that, under suitable hypotheses on $F$, this problem has a family of non self intersecting solutions $u_D$, which are at finite distance from a plane of slope $(\o,0,\dots,0)$ with $\o$ irrational. These solutions depend on a real parameter $D$; if $D\not=D^\prime$, then the closures of the integer translates of $u_D$ and of $u_{D^\prime}$ do not intersect.

Bessi, U. (2005). Many solutions of elliptic problems on R^n of irrational slope. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 30, 1773-1804 [10.1080/03605300500299992].

Many solutions of elliptic problems on R^n of irrational slope

BESSI, Ugo
2005-01-01

Abstract

We consider the problem $-\Delta u+F_u(x,u)=0$ on $\R^n$, where $F$ is a smooth function periodic of period 1 in all its variables. We show that, under suitable hypotheses on $F$, this problem has a family of non self intersecting solutions $u_D$, which are at finite distance from a plane of slope $(\o,0,\dots,0)$ with $\o$ irrational. These solutions depend on a real parameter $D$; if $D\not=D^\prime$, then the closures of the integer translates of $u_D$ and of $u_{D^\prime}$ do not intersect.
Bessi, U. (2005). Many solutions of elliptic problems on R^n of irrational slope. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 30, 1773-1804 [10.1080/03605300500299992].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/143321
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