Abstract
We consider a nonlinear Neumann problem with a reaction term which exhibits an asymmetric behavior near +∞ and near −∞. Namely, it is asymptotically superlinear at +∞ and linear at −∞. Using variational methods based on critical point theory, together with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative).
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Papageorgiou, N.S., Smyrlis, G. A multiplicity theorem for Neumann problems with asymmetric nonlinearity. Annali di Matematica 189, 253–272 (2010). https://doi.org/10.1007/s10231-009-0108-7
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DOI: https://doi.org/10.1007/s10231-009-0108-7