An abstract version of the resonance theorem
B. Przeradzki (1991)
Annales Polonici Mathematici
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B. Przeradzki (1991)
Annales Polonici Mathematici
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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.
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.
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.
Peter Hess (1977)
Mathematische Zeitschrift
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W. Hackbusch (1979)
Numerische Mathematik
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Peter Hess, Bernhard Ruf (1978/79)
Mathematische Zeitschrift
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Uraltseva, N. N.
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Giovanni Cimatti (2009)
Bollettino dell'Unione Matematica Italiana
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The voltage-current characteristics of two classes of nonlinear resistors (varistors and thermistors) modelled as three-dimensional bodies is derived from the corresponding systems of nonlinear elliptic boundary value problems. Theorems of existence and uniqueness of solutions are presented, together with certain properties of monotonicity of the conductance.
Nicolai V. Krylov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Heinz Brill (1976)
Mathematische Annalen
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Martin Schechter (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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