AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator
which is locally elliptic and positively 1-homogeneous.
Generalizing [H. Berestycki and L. Rossi,
Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains,
Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues
and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.