Affiliation:
1. Department of Mathematics , Indian Institute of Science Education and Research , Dr. Homi Bhabha Road , Pune 411008 , India
Abstract
Abstract
We study the generalized eigenvalue problem in
ℝ
N
{\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.
Subject
Applied Mathematics,Analysis
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