$\Delta u=0$ where $x>0,y\in[0,1]$
$u$ is periodic in $y$, i.e., $u(x,0)=u(x,1)$
$u$ is constant at $x=0$, i.e., $u(0,y)=1$
$u$ stays bound at infinity i.e., $u(+\infty,y)=0$
Does there exist any solution that satisfies all the above boundary conditions? I tried separation of variable and Fourier series which don't seem to work.