High multiplicity of positive solutions for superlinear indefinite problems with homogeneous Neumann boundary conditions.

@article{Tellini2017HighMO,
  title={High multiplicity of positive solutions for superlinear indefinite problems with homogeneous Neumann boundary conditions.},
  author={A. Tellini},
  journal={arXiv: Classical Analysis and ODEs},
  year={2017}
}
  • A. Tellini
  • Published 2017
  • Mathematics
  • arXiv: Classical Analysis and ODEs
We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The sign-changing weight in front of the nonlinearity is taken to be piecewise constant, which allows to perform a sharp phase-plane analysis, firstly to study the sets of points reached at the end of the regions where the weight is negative, and then to connect such sets… Expand

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