An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems

Abstract

We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A careful adaptation of well known variational methods is required to deal with the possible existence of negative eigenvalues.

arXiv admin note: text overlap with arXiv:2207.14008