Neumann problems resonant at zero and infinity |
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Authors: | Leszek Gasiński Nikolaos S Papageorgiou |
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Institution: | 1. Institute of Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30-348, Kraków, Poland 2. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece
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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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