We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Carathéodory function exhibiting linear growth near ±∞. We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.
Papageorgiou, N., Vetro, C., Vetro, F. (2017). Robin problems with general potential and double resonance. APPLIED MATHEMATICS LETTERS, 68, 122-128 [10.1016/j.aml.2017.01.003].
Robin problems with general potential and double resonance
VETRO, Calogero;VETRO, Francesca
2017-01-01
Abstract
We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Carathéodory function exhibiting linear growth near ±∞. We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.
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