Giovanni Anello (2005)
Annales Polonici Mathematici
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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.
Mikhail Borsuk, Krzysztof Żyjewski (2011)
Applicationes Mathematicae
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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
B. Przeradzki (1991)
Annales Polonici Mathematici
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B. Szafirski (1967)
Colloquium Mathematicae
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Peter Hess, Bernhard Ruf (1978/79)
Mathematische Zeitschrift
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D. Kinderlehrer, L. Nirenberg, J. Spruck (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Devdariani, G. (2001)
Bulletin of TICMI
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Aissa Aibeche, Angelo Favini, Chahrazed Mezoued (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we consider an abstract elliptic differential problem where the equation and the boundary conditions may contain a spectral parameter. We first prove that this problem generates an isomorphism between appropriate spaces and we establish a more precise estimate called coerciveness estimate with defect. The results obtained are applied to study some classes of elliptic, and also possibly degenerate, problems.
J. González (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Krystyna Szafraniec (1989)
Annales Polonici Mathematici
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Andrew Bremner (2003)
Acta Arithmetica
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Giuliano Bratti (1977)
Rendiconti del Seminario Matematico della Università di Padova
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K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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Chi-ping Lau (1985)
Manuscripta mathematica
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Tiantian Qiao, Weiguo Li, Kai Liu, Boying Wu (2014)
Annales Polonici Mathematici
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The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.