Resumen
In this work we provide local bifurcation results for equations involving the p-Laplacian in balls. We analyze the continua n of radial solutions emanating from (n, p, 0), {n, p} being the radial eigenvalues of -p. First, we show that the only nontrivial solutions close to (n, p, 0) lie on a continuous curve, thus extending the Crandall-Rabinowitz theorem. Second, it is proved that n\{(n, p, 0)} splits into two unbounded connected pieces, characterized by their nodal properties thus sharpening previous results.