Robin problems with general potential and double resonance. (June 2017)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca
• Is Part Of: Applied mathematics letters. Volume 68(2017:Jun.)
• Page Start: 122
• Page End: 128
• Publication Date: 2017-06
• Subjects: Indefinite and unbounded potential -- Double resonance critical groups -- Regularity theory -- Robin boundary condition; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.01.003
• Languages: English
• ISSNs: 0893-9659

Abstract

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.