English

Principal eigenvalues of a class of nonlinear integro-differential operators

Analysis of PDEs 2018-03-20 v2

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.

Keywords

Cite

@article{arxiv.1803.02040,
  title  = {Principal eigenvalues of a class of nonlinear integro-differential operators},
  author = {Anup Biswas},
  journal= {arXiv preprint arXiv:1803.02040},
  year   = {2018}
}

Comments

Theorem 2.6 updated