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.
2017
Settore MAT/05 - Analisi Matematica
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/226097
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