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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 3, Pages 619–634 (Mi smj2224)  
Existence of solutions to resonant elliptic boundary value problems with unbounded discontinuous nonlinearities

M. G. Lepchinskiĭ

Chelyabinsk State University, Chelyabinsk
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Abstract: We consider the situation when a resonant elliptic boundary value problem with an unbounded discontinuous nonlinearity is an idealization of a distributed system with continuous nonlinearities with respect to the phase variable and possessing narrow regions in the phase variable domain where the changes of nonlinear parameters are intractable. We study the existence of solutions to problems of this type.
Keywords: resonant elliptic problem, discontinuous nonlinearities, sublinear growth, Landesman–Lazer conditions, variational method.
Received: 24.09.2007
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 3, Pages 487–500
DOI: https://doi.org/10.1134/S0037446611030116
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. G. Lepchinskiǐ, “Existence of solutions to resonant elliptic boundary value problems with unbounded discontinuous nonlinearities”, Sibirsk. Mat. Zh., 52:3 (2011), 619–634; Siberian Math. J., 52:3 (2011), 487–500
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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