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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 195, Issue 4, pp 1207–1235 | Cite as

Nonlinear Robin problems with a reaction of arbitrary growth

  • Nikolaos S. Papageorgiou
  • Patrick Winkert
Article

Abstract

We consider Robin problems driven by a nonhomogeneous differential operator involving a reaction that has zeros and no global growth restriction. Using variational methods together with truncation and perturbation techniques as well as Morse theory, we prove multiplicity theorems with precise sign information for all the solutions.

Keywords

Constant sign and nodal solutions Reaction with zeros  Nonlinear regularity Nonlinear maximum principle Superlinear near zero Critical groups 

Mathematics Subject Classification

35J20 35J60 35J92 58E05 

Notes

Acknowledgments

The authors wish to thank the referee for his/her corrections and insightful remarks that helped improve the paper.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany

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