Principal eigenvalues of a class of nonlinear integro-differential operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Biswas, Anup¹ 

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

关键词: Principal eigenvalue;    Fractional Laplacian;    Nonlocal operators;    Ground state;    Anti-maximum principle;    Dirichlet problem;   

DOI  :  10.1016/j.jde.2019.11.011

来源: Elsevier

【 摘 要 】

We consider a class of nonlinear integro-differential operators and prove existence of two principal (half) eigenvalues in bounded smooth domains with exterior Dirichlet condition. We then establish simplicity of the principal eigenfunctions in viscosity sense, maximum principles, continuity property of the principal eigenvalues with respect to domains etc. We also prove an anti-maximum principle and study existence result for some nonlinear problem via Rabinowitz bifurcation-type results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free