The Klein Gordon equation of the form:
$\Delta u+ \lambda u^p=0$
is been studied for $p = 2$? 
(i.e.$\Delta u+ \lambda u^2=0$)
If yes are there references?



Klein Gordon equation - references
This is a nonlinear Klein-Gordon equation of the type
$$ \Delta u = f(u) $$
which, at least in $1+1$ dimensions has been studied for several functions $f$; although the most interesting seem to be when $f$ are exponential or trigonometric, e.g., [sine-Gordon equation](https://en.wikipedia.org/wiki/Sine-Gordon_equation) or approximations thereof.


The case where $f(u) = u^n$ appears in §7.1.1.1 of the Handbook of nonlinear PDEs by Polyanin and Zaitsev.



```
@book {MR2865542,
    AUTHOR = {Polyanin, Andrei D. and Zaitsev, Valentin F.},
     TITLE = {Handbook of nonlinear partial differential equations},
   EDITION = {Second},
 PUBLISHER = {CRC Press, Boca Raton, FL},
      YEAR = {2012},
     PAGES = {xxxvi+876},
      ISBN = {978-1-4200-8723-9},
   MRCLASS = {35-00 (35C05)},
  MRNUMBER = {2865542},
}

```

