  We consider the nonlinear string equation with Dirichlet boundary conditions
$u_{xx}-u_{tt}=\phi(u)$, with $\phi(u)=\Phi u^{3} + O(u^{5})$ odd and analytic,
$\Phi\neq0$, and we construct small amplitude periodic solutions with frequency
$\o$ for a large Lebesgue measure set of $\o$ close to 1. This extends previous
results where only a zero-measure set of frequencies could be treated (the ones
for which no small divisors appear). The proof is based on combining the
Lyapunov-Schmidt decomposition, which leads to two separate sets of equations
dealing with the resonant and nonresonant Fourier components, respectively the
Q and the P equations, with resummation techniques of divergent powers series,
allowing us to control the small divisors problem. The main difficulty with
respect the nonlinear wave equations $u_{xx}-u_{tt}+ M u = \phi(u)$, $M\neq0$,
is that not only the P equation but also the Q equation is infinite-dimensional
