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Arbitrarily Small Nodal Solutions for Parametric Robin (p, q)-Equations Plus an Indefinite Potential

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Abstract

We consider a nonlinear Robin problem driven by the (p, q)-Laplacian plus an indefinite potential term and with a parametric reaction term. Under minimal conditions on the reaction function, which concern only its behavior near zero, we show that, for all λ > 0 small, the problem has a nodal solution \({y_\lambda } \in {C^1}(\bar \Omega )\) and we have yλ → 0 \({C^1}(\bar \Omega )\) as λ → 0+.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Viale A. Doria, 6, 95125, Catania, Italy

    Salvatore Leonardi

  2. Department of Mathematics, Technical University, Zorografou Campus, Athens, 15780, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Salvatore Leonardi
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  2. Nikolaos S. Papageorgiou
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Corresponding authors

Correspondence to Salvatore Leonardi or Nikolaos S. Papageorgiou.

Additional information

This work has been supported by Piano della Ricerca di Ateneo 2020–2022— PIACERI: Project MO.S.A.I.C. “Monitoraggio satellitare, modellazioni matematiche e soluzioni architettoniche e urbane per lo studio, la previsione e la mitigazione delle isole di calore urbano”, Project EEEP&DLaD. S. Leonardi is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Leonardi, S., Papageorgiou, N.S. Arbitrarily Small Nodal Solutions for Parametric Robin (p, q)-Equations Plus an Indefinite Potential. Acta Math Sci 42, 561–574 (2022). https://doi.org/10.1007/s10473-022-0210-0

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  • DOI: https://doi.org/10.1007/s10473-022-0210-0

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