  The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional
$R^1\times S^1$ spacetime with compactified space coordinate are investigated
in the presence of the isospin chemical potential $\mu_I$. The consideration is
performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of
colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the
circumference $S^1$) the pion condensation phase is realized for arbitrary
small nonzero $\mu_I$. At finite values of $L$, the phase portraits of the
model in terms of parameters $\nu\sim\mu_I$ and $\lambda\sim 1/L$ are obtained
both for periodic and antiperiodic boundary conditions of the quark field. It
turns out that in the plane $(\lambda,\nu)$ there is a strip
$0\le\lambda<\lambda_c$ which lies as a whole inside the pion condensed phase.
In this phase the pion condensation gap is an oscillating function vs both
$\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).
