Existence of a minimal solution and a maximal solution of a nonlinear elliptic boundary value problem of the fourth order
Jan Bochenek (1985)
Annales Polonici Mathematici
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Displaying similar documents to “On extremal solutions to infinite dimensional non-linear second order systems”
Existence of a minimal solution and a maximal solution of a nonlinear elliptic boundary value problem of the fourth order
Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner 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.
The first boundary problem for a degenerate elliptic system.
Devdariani, G. (2001)
Bulletin of TICMI
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An abstract version of the resonance theorem
B. Przeradzki (1991)
Annales Polonici Mathematici
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Maximal and Minimal Solutions of Elliptic Differential Equations with Discontinuous Non-Linearities.
Charles A. Stuart (1978)
Mathematische Zeitschrift
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An overdetermined elliptic problem in a domain with countably rectifiable boundary
Przemysław Górka (2007)
Colloquium Mathematicae
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We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.
Remark on a uniqueness result for a boundary value problem of eighth-order.
Danet, Cristian-Paul (2009)
Applied Mathematics E-Notes [electronic only]
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Remarks on a three-point boundary value problem in a differential equation of the third order
M. Greguš (1974)
Annales Polonici Mathematici
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A boundary value problem for non-linear differential equations with a retarded argument
Józef Wenety Myjak (1973)
Annales Polonici Mathematici
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Regularity in elliptic free boundary problems. II. Equations of higher order
D. Kinderlehrer, L. Nirenberg, J. Spruck (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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On a Superlinear Elliptic Boundary Value Problem.
Peter Hess, Bernhard Ruf (1978/79)
Mathematische Zeitschrift
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Boundary trace of positive solutions of nonlinear elliptic inequalities
Moshe Marcus, Laurent Véron (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of in a smooth domain under very general assumptions on . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the...
On some elliptic boundary-value problems with discontinuous nonlinearities
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.