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Annali di Matematica Pura ed Applicata

, Volume 191, Issue 3, pp 395–430 | Cite as

Neumann problems resonant at zero and infinity

  • Leszek Gasiński
  • Nikolaos S. Papageorgiou
Open Access
Article

Abstract

We consider a semilinear Neumann problem with a reaction which is resonant at both zero and ±∞. Using a combination of methods from critical point theory, together with truncation techniques, the use of upper–lower solutions and of the Morse theory (critical groups), we show that the problem has at least five nontrivial smooth solutions, four of which have constant sign (two positive and two negative).

Keywords

Resonance at zero and infinity Critical point theory Morse theory Truncation techniques Regularity theory Multiple solutions Solutions of constant sign 

Mathematics Subject Classification (2000)

35J20 35J60 58E05 

Notes

Acknowledgments

The authors would like to thank the referee for their corrections and remarks.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

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