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Non-trivial solutions of local and non-local Neumann boundary-value problems

  • Gennaro Infante (a1), Paolamaria Pietramala (a1) and F. Adrián F. Tojo (a2)

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We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

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