  We investigate the Chandrasekhar mass limit for white dwarfs in various
models of $f(R)$ gravity. Two equations of state for stellar matter are used:
simple relativistic polytropic equation with polytropic index $n=3$ and the
realistic Chandrasekhar equation of state. For calculations it is convenient to
use the equivalent scalar-tensor theory in the Einstein frame and then to
return in the Jordan frame picture. For white dwarfs we can neglect terms
containing relativistic effects from General Relativity and we consider the
reduced system of equations. Its solution for any model of $f(R)=R+\beta R^{m}$
($m\geq 2$, $\beta>0$) gravity leads to the conclusion that the stellar mass
decreases in comparison with standard General Relativity. For realistic
equations of state we find that there is a value of the central density for
which the mass of white dwarf peaks. Therefore, in frames of modified gravity
there is lower limit on the radius of stable white dwarfs and this minimal
radius is greater than in General Relativity.
