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Izvestiya: Mathematics, 2011, Volume 75, Issue 1, Pages 157–176
DOI: https://doi.org/10.1070/IM2011v075n01ABEH002530 (Mi im3955) 		 
Existence theorems for resonance boundary-value problems of elliptic type with discontinuous unbounded non-linear parts

E. A. Rozhdestvenskaya

Chelyabinsk State University
English version PDF (358 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2011v075n01ABEH002530
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.
Received: 26.08.2008
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35J66, 35J15, 35R05, 35B34
Language: English
Original paper language: Russian
Citation: E. A. Rozhdestvenskaya, “Existence theorems for resonance boundary-value problems of elliptic type with discontinuous unbounded non-linear parts”, Izv. Math., 75:1 (2011), 157–176
Citation in format AMSBIB
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\vol 75
\issue 1
\pages 157--176
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:202
    English version PDF:12
    References:82
    First page:30
     
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