Multiple solutions with sign information for semilinear Neumann problems with convection

Abstract

We consider a semilinear Neumann problem with convection. We assume that the drift coefficient is indefinite. Using the theory of nonlinear operators of monotone type, together with truncation and comparison techniques and flow invariance arguments, we prove a multiplicity theorem producing three nontrivial smooth solutions (positive, negative and nodal).

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Acknowledgements

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

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Correspondence to Francesca Vetro.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. Multiple solutions with sign information for semilinear Neumann problems with convection. Rev Mat Complut 33, 19–38 (2020). https://doi.org/10.1007/s13163-019-00312-3

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Keywords

  • Indefinite drift coefficient
  • Constant sign and nodal solutions
  • Extremal constant sign solutions
  • Flow invariance
  • Convection

Mathematics Subject Classification

  • 35J60
  • 35J92