### Compactness Method in the Finite Element Theory of Nonlinear Elliptic Problems.

Miloslav Feistauer, Alexander Zenisek (1987/88)

Numerische Mathematik

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Miloslav Feistauer, Alexander Zenisek (1987/88)

Numerische Mathematik

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W. Hackbusch (1979)

Numerische Mathematik

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Miloslav Feistauer, Alexander Zenisek (1986/87)

Numerische Mathematik

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N.L. Schryer (1971/72)

Numerische Mathematik

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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.

P. KEAST (1968)

Numerische Mathematik

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I.G. Stratis (1993)

Publications de l'Institut Mathématique

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Michal Křížek, Liping Liu (1996)

Applicationes Mathematicae

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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.

Edward N. Dancer, Shusen Yan (2007)

Bollettino dell'Unione Matematica Italiana

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We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.

Peter Hess, Bernhard Ruf (1978/79)

Mathematische Zeitschrift

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Nicolai V. Krylov (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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