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 50 条

[31] PRINCIPAL EIGENVALUES OF GENERALIZED CONVOLUTION OPERATORS ON THE CIRCLE AND SPREADING SPEEDS OF NONCOMPACT EVOLUTION SYSTEMS IN PERIODIC MEDIA
Ding, Weiwei
Liang, Xing
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (01) : 855 - 896
[32] The Spectral Function and Principal Eigenvalues for Schrödinger Operators
Wolfgang Arendt
Charles J. K. Batty
Potential Analysis, 1997, 7 : 415 - 436
[33] Principal eigenvalues and eigenfunctions for fully nonlinear equations in punctured balls
Birindelli, Isabeau
Demengel, Francoise
Leoni, Fabiana
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2024, 186 : 74 - 102
[34] Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions
Patrizi, Stefania
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (01): : 79 - 107
[35] Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions
Stefania Patrizi
Nonlinear Differential Equations and Applications NoDEA, 2009, 16 : 79 - 107
[36] Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
Chen, Hua
Luo, Peng
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (03) : 2831 - 2852
[37] Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators
Kozlov, Vladimir
Thim, Johan
JOURNAL OF SPECTRAL THEORY, 2016, 6 (01) : 99 - 135
[38] Estimates of Dirichlet eigenvalues for a class of sub-elliptic operators
Chen, Hua
Chen, Hong-Ge
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2021, 122 (06) : 808 - 847
[39] Harnack inequality and principal eigentheory for general infinity Laplacian operators with gradient in RN and applications
Biswas, Anup
Hoang-Hung Vo
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (04)
[40] Principal eigenvalues of elliptic problems with singular potential and bounded weight function
Godoy, Tomas
CONSTRUCTIVE MATHEMATICAL ANALYSIS, 2023, 6 (02): : 107 - 127

← 1 2 3 4 5 →