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arXiv · 2004.06269

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

Anup Biswas·Prasun Roychowdhury
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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.

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Anup Biswas, Prasun Roychowdhury. 2020-04-14. Generalized principal eigenvalues of convex nonlinear elliptic operators in $\mathbb{R}^N$. https://doi.org/10.1515/acv-2020-0035

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