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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 1, Pages 161–180 (Mi izv3955)  

Existence theorems for resonance boundary-value problems of elliptic type with discontinuous unbounded non-linear parts

E. A. Rozhdestvenskaya

Chelyabinsk State University

Abstract: The existence of a solution of the Dirichlet problem for a second order elliptic equation with non-linear part discontinuous in the phase variable is proved in the cases of resonance on the left and resonance on the right of the first eigenvalue of the differential operator in the situation where the Landesman–Lazer conditions do not hold.

Keywords: resonance elliptic boundary-value problems, discontinuous non-linearities, Landesman–Lazer condition.

DOI: https://doi.org/10.4213/im3955

Full text: PDF file (632 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:1, 157–176

Bibliographic databases:

Document Type: Article
UDC: 517.95
MSC: 35J66, 35J15, 35R05, 35B34
Received: 26.08.2008

Citation: E. A. Rozhdestvenskaya, “Existence theorems for resonance boundary-value problems of elliptic type with discontinuous unbounded non-linear parts”, Izv. RAN. Ser. Mat., 75:1 (2011), 161–180; Izv. Math., 75:1 (2011), 157–176

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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