Generalized principal eigenvalues of convex nonlinear elliptic operators in ${\mathbb{R}}^N$

Abstract

We 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 article of Berestycki and Rossi in [Comm. Pure Appl. Math. 68 (2015), no. 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.

arXiv comment21 pages. To appear in Adv. Calc. Var

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Cited by in corpus (1)

• Generalized principal eigenvalues on ${\mathbb{R}}^d$ of second order elliptic operators with rough nonlocal kernels