S-Shaped Connected Component of Positive Solutions for a Minkowski-Curvature Dirichlet Problem with Indefinite Weight

Abstract

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions for a Minkowski-curvature Dirichlet problem with indefinite weight. By figuring the shape of unbounded continua of solutions, we show the existence and multiplicity of positive solutions with respect to the parameter \(\lambda \). In particular, we obtain the existence of at least three positive solutions for \(\lambda \) being in a certain interval.

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Correspondence to Zhiqian He.

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Z. He: Supported by the NSFC (No. 11861056).

Communicated by Majid Gazor.

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He, Z., Miao, L. S-Shaped Connected Component of Positive Solutions for a Minkowski-Curvature Dirichlet Problem with Indefinite Weight. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-020-00512-4

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Keywords

  • Mean curvature operator
  • Indefinite weight
  • Three positive solutions
  • Bifurcation

Mathematics Subject Classification

  • 34C23
  • 34B10
  • 34B18