Stefania Patrizi (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
Stefania Patrizi (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
Jifeng Chu, Daqing Jiang, Donal O'Regan, R. P. Agarwal (2005)
Applicationes Mathematicae
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We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
Huzihiro Araki (1975)
Recherche Coopérative sur Programme n°25
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Zhai, Chengbo, Song, Ruipeng (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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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.
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.
J. Chabrowski (2007)
Colloquium Mathematicae
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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
Hichem Ben-El-Mechaiekh, Robert Dimand (2007)
Banach Center Publications
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Peter Hess, Stefan Senn (1981)
Mathematische Annalen
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Yoshihiro Nakamura, Fumio Hiai (1987)
Mathematische Zeitschrift
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Otto Moeschlin (2006)
Banach Center Publications
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Andrzej Granas, Ronald Guenther, John Lee
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CommentsThis tract is intended to be accessible to a broad spectrum of readers. Those with out much previous experience with differential equations might find it profitable (when the need arises) to consult one of the following standard texts: Coddington-Levinson [17], Hale [35], Hartman [38], Mawhin-Rouche [61]. The bibliography given below is restricted mostly to the problems discussed in the tract or closely related topics. A small number of additional references are included however...
H. Woźniakowski (1971)
Applicationes Mathematicae
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Farrukh Mukhamedov, Hasan Akin, Seyit Temir (2006)
Colloquium Mathematicae
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We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.