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Double-phase problems and a discontinuity property of the spectrum


Authors: Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu and Dušan D. Repovš
Journal: Proc. Amer. Math. Soc. 147 (2019), 2899-2910
MSC (2010): Primary 35D30; Secondary 35J60, 35P30
DOI: https://doi.org/10.1090/proc/14466
Published electronically: March 15, 2019
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Abstract: We consider a nonlinear eigenvalue problem driven by the sum of $ p$ and $ q$-Laplacians. We show that the problem has a continuous spectrum. Our result reveals a discontinuity property for the spectrum of a parametric ($ p,q$)-differential operator as the parameter $ \beta $ goes to $ 1^-$.


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Additional Information

Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece; Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia
Email: npapg@math.ntua.gr

Vicenţiu D. Rădulescu
Affiliation: Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland; Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia; Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Email: vicentiu.radulescu@imar.ro

Dušan D. Repovš
Affiliation: Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana; Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia
Email: dusan.repovs@guest.arnes.si

DOI: https://doi.org/10.1090/proc/14466
Keywords: Nehari manifold, continuous spectrum, nonlinear regularity
Received by editor(s): August 28, 2018
Published electronically: March 15, 2019
Additional Notes: This research was supported by the Slovenian Research Agency grants P1-0292, J1-8131, J1-7025, N1-0064, and N1-0083.
The second author acknowledges the support through the Project MTM2017-85449-P of the DGISPI (Spain).
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society