This paper establishes lower and upper bounds for the radial eigenvalues of nonlinear elliptic systems defined in appropriate annular domains of \(\mathbb {R}^N\) . For the problem, we will prove a result in the sense of a conjecture proposed by Nápoli and Pinasco in the paper Estimates for eigenvalues of quasilinear elliptic systems, J. Diff. Eq. 227 (2006), 102–115, when we are in certain domains of \(\mathbb {R}^N\) . Moreover, we obtain a hyperbolic type function defining a region that contains all the generalized eigenvalues (whether variational or not), and with general hypotheses, the proof is carried out via ABP estimate for the p-Laplacian operator.
