A nonexistence theorem for an equation with critical Sobolev exponent in the half space.
H. Berestycki, M. Gross, F. Pacella (1992)
Manuscripta mathematica
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H. Berestycki, M. Gross, F. Pacella (1992)
Manuscripta mathematica
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J. Chabrowski, P. Drábek (2002)
Studia Mathematica
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We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.
M. Struwe, A. Ambrosetti (1986)
Manuscripta mathematica
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J. Chabrowski, E. Tonkes (2003)
Annales Polonici Mathematici
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We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.
Myriam Comte, Mariette C. Knaap (1990)
Manuscripta mathematica
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J. Chabrowski, Jianfu Yang (2001)
Colloquium Mathematicae
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We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
Gazzola, Filippo (1998)
Abstract and Applied Analysis
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Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)
Applicationes Mathematicae
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We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.
Molle, Riccardo, Passaseo, Donato (2004)
Abstract and Applied Analysis
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Druet, Olivier, Hebey, Emmanuel, Robert, Frédéric (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Gabriella Tarantello (1993)
Manuscripta mathematica
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C. Bandle, L.A. Peletier (1988)
Mathematische Annalen
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A. Capozzi, D. Fortunato, G. Palmieri (1985)
Annales de l'I.H.P. Analyse non linéaire
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J. Chabrowski, Jianfu Yang (2003)
Rendiconti del Seminario Matematico della Università di Padova
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Giovanni Mancini, Roberta Musina (1987)
Manuscripta mathematica
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Michael Struwe (2000)
Journal of the European Mathematical Society
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For semilinear elliptic equations of critical exponential growth we establish the existence of positive solutions to the Dirichlet problem on suitable non-contractible domains.