I need to solve the following equation for $x$: 
$$x + a x(x)=l,$$

where $a$ is a constant and $l$ and $x$ are vectors. By $x(x)$, I mean that every element in $x$ is shifted according to itself or in other words $x$ is applied to itself. For example let's say $x=[x\_1, x\_2, x\_3, x\_4, x\_5]=[-4, 1, 0, 2, 1]$, then $x(x)=[1, 2, 0, 1, -4]$. So, $x\_1$ is basically shifted by $x\_1$ and thus it is located at last in $x(x)$; $x\_2$ is shifted by $x\_2$ and thus it is located at first. 

Note that the elements of $x$ are not integers. This is only an example for better understanding the notation. $x$'s elements are "real" numbers. In case of real values, interpolation will be performed for calculating $x(x)$.  

Also, note that the direction of shift is (+) $\leftarrow$ (-).

Any comments or ideas is very very much appreciated. Also, I was wondering if there is a standard mathematics notation for what I have shown here as $x(x)$.