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Positive Solutions for Nonlinear Dirichlet Problems with Convection

Applied Mathematics & Optimization volume 82, pages 451–470 (2020)Cite this article

Abstract

We consider a nonlinear Dirichlet problem driven by the p-Laplacian, a convection term and a \((p-1)\)-sublinear perturbation. First we assume that the coefficient in the convection term (drift coefficient) is sign changing. Using the theory of nonlinear operators of monotone type together with suitable truncation and comparison techniques we prove the existence of a positive smooth solution. When the drift coefficient is nonnegative, we are able to relax the conditions on the data of the problem.

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Acknowledgements

The authors wish to thank the two referees for their corrections and helpful remarks.

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Authors and Affiliations

  1. College of Mathematics, Shandong Normal University, Jinan, Shandong, China

    Shouchuan Hu

  2. Department of Mathematics, Missouri State University, Springfield, MO, 65804, USA

    Shouchuan Hu

  3. Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece

    Nikolas S. Papageorgiou

Authors
  1. Shouchuan Hu
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  2. Nikolas S. Papageorgiou
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Correspondence to Nikolas S. Papageorgiou.

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Hu, S., Papageorgiou, N.S. Positive Solutions for Nonlinear Dirichlet Problems with Convection. Appl Math Optim 82, 451–470 (2020). https://doi.org/10.1007/s00245-018-9534-5

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  • DOI: https://doi.org/10.1007/s00245-018-9534-5

Keywords

  • Convection term
  • Indefinite drift coefficient
  • Nonlinear regularity
  • Nonlinear maximum principle
  • Truncation
  • Nonlinear Krein–Rutman theorem

Mathematics Subject Classification

  • 35J60
  • 35J92