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.
An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems / Giovannardi G.; Mugnai D.; Vecchi E.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - ELETTRONICO. - 527:(2023), pp. 0-0. [10.1016/j.jmaa.2023.127442]
An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems
Giovannardi G.;Mugnai D.;
2023
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.
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