A Local Bifurcation Theorem for Degenerate Elliptic Equations With Radial Symmetry

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 (λn, p, 0), {λn, p} being the radial eigenvalues of −Δp. First, we show that the only nontrivial solutions close to (λn, p, 0) lie on a continuous curve, thus extending the Crandall–Rabinowitz theorem. Second, it is proved that n\{(λn, p, 0)} splits into two unbounded connected pieces, characterized by their nodal properties thus sharpening previous results.