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).
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Acknowledgments
The authors would like to thank the referee for their corrections and remarks.
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This research has been partially supported by the Ministry of Science and Higher Education of Poland under Grant no. N201 542438.
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Gasiński, L., Papageorgiou, N.S. Neumann problems resonant at zero and infinity. Annali di Matematica 191, 395–430 (2012). https://doi.org/10.1007/s10231-011-0188-z
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DOI: https://doi.org/10.1007/s10231-011-0188-z
Keywords
- Resonance at zero and infinity
- Critical point theory
- Morse theory
- Truncation techniques
- Regularity theory
- Multiple solutions
- Solutions of constant sign