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Remarks on variational methods and lower-upper solutions

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

The presence of lower and upper solutions to semilinear elliptic equations is linked to some variational properties of the associated action functionals. We exploit this variational characterization to find existence and multiplicity of solutions when multiple lower and upper solutions are given in various ordering relations.

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Authors and Affiliations

  1. Università di Milano, via Saldini 50-I-20133 Milano, Italy , , , , , , IT

    Monica Conti & Luca Merizzi

  2. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, , , , ,

    Susanna Terracini

Authors
  1. Monica Conti
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  2. Luca Merizzi
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  3. Susanna Terracini
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Received July 1998

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Conti, M., Merizzi, L. & Terracini, S. Remarks on variational methods and lower-upper solutions. NoDEA, Nonlinear differ. equ. appl. 6, 371–393 (1999). https://doi.org/10.1007/s000300050009

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  • DOI: https://doi.org/10.1007/s000300050009

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