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Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator

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Abstract

This work is concerned with the existence of solutions to parametric elliptic equations driven by a nonhomogeneous differential operator with a nonhomogeneous Neumann boundary condition. The assumptions on the operator involve the \(p\)-Laplacian, the \((p,q)\)-Laplacian, and the generalized \(p\)-mean curvature differential operator. Based on variational tools combined with truncation and comparison techniques we prove the existence of at least three nontrivial solutions provided the parameter is sufficiently large whereby the first solution is positive, the second one is negative and the third one has changing sign (nodal).

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 , Berlin, Germany

    Said El Manouni & Patrick Winkert

  2. Department of Mathematics, National Technical University, Zografou Campus, 15780 , Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Said El Manouni
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  2. Nikolaos S. Papageorgiou
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  3. Patrick Winkert
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Correspondence to Patrick Winkert.

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Communicated by A. Jüngel.

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El Manouni, S., Papageorgiou, N.S. & Winkert, P. Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator. Monatsh Math 177, 203–233 (2015). https://doi.org/10.1007/s00605-014-0649-8

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  • DOI: https://doi.org/10.1007/s00605-014-0649-8

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