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Jan Chabrowski (2004)
Colloquium Mathematicae
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We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.
J. Chabrowski (2002)
Bollettino dell'Unione Matematica Italiana
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In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
Jan Chabrowski, Bernhard Ruf (2007)
Colloquium Mathematicae
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We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.
J. Chabrowski, Jianfu Yang (2003)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Gabriella Tarantello (1993)
Manuscripta mathematica
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Myriam Comte, Mariette C. Knaap (1990)
Manuscripta mathematica
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Anna Maria Candela, Monica Lazzo (1994)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this paper we study the influence of the domain topology on the multiplicity of solutions to a semilinear Neumann problem. In particular, we show that the number of positive solutions is stable under small perturbations of the domain.
Jan Chabrowski (2011)
Colloquium Mathematicae
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We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.
Jan Chabrowski, Kyril Tintarev (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
Daniele Castorina, Gianni Mancini (2003)
Rendiconti del Seminario Matematico della Università di Padova
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Jan Chabrowski, Jianfu Yang (2005)
Annales Polonici Mathematici
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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.
Manuel del Pino, Monica Musso, Angela Pistoia (2005)
Annales de l'I.H.P. Analyse non linéaire
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Lucas C. van der Merwe, Cristine M. Mynhardt, Teresa W. Haynes (2001)
Discussiones Mathematicae Graph Theory
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Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.