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Monatshefte für Mathematik

, Volume 177, Issue 2, pp 203–233 | Cite as

Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator

  • Said El Manouni
  • Nikolaos S. Papageorgiou
  • Patrick Winkert
Article

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).

Keywords

Constant sign and nodal solutions Nonlinear regularity Critical point of mountain pass type Extremal solutions Local minimizers Maximum principle 

Mathematics Subject Classification (2010)

35J20 35J60 35J92 58E05 

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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Said El Manouni
    • 1
  • Nikolaos S. Papageorgiou
    • 2
  • Patrick Winkert
    • 1
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

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