Global bifurcation and nodal solutions of N-dimensional p-Laplacian in unit ball

摘要

We are concerned with determining values of γ, for which there exist radial nodal solutions of the boundary-value problem Δ_pu + γa(x)f(u) = 0 in B, u = 0 on {partial deriv}B, where B is the unit open ball in R~N with N≥1. The proofs of our main results are based upon bifurcation techniques. In particular, we establish the global bifurcation theory for a second-order weighted p-Laplacian eigenvalue problem in B.