Generalized principal eigenvalues of convex nonlinear elliptic operators in RN

被引：1

作者：

Biswas, Anup ^{[1
]}

Roychowdhury, Prasun ^{[1
]}

机构：

[1] Indian Inst Sci Educ & Res, Dept Math, Dr Homi Bhabha Rd, Pune 411008, Maharashtra, India

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2022年 / 15卷 / 04期

关键词：

Fully nonlinear operators; principal eigenvalue; Dirichlet problem; half-eigenvalues; uniqueness; MAXIMUM PRINCIPLE; VARIATIONAL FORMULA; EQUATIONS; BIFURCATION; BOUNDARY;

D O I：

10.1515/acv-2020-0035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the generalized eigenvalue problem in 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), 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.

引用

页码：673 / 691

页数：19

共 27 条

[1]

Arapostathis A, 2020, Arxiv, DOI arXiv:1903.08346

[2] A VARIATIONAL FORMULA FOR RISK-SENSITIVE CONTROL OF DIFFUSIONS IN Rd [J].