Principal eigenvalues of a class of nonlinear integro-differential operators

2018/03/06 by Anup Biswas, Biswas, Anup
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1803.02040

Theorem 2.6 updated

arxiv created 2018/03/17 · arxiv updated 2018/03/20

Abstract

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.

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