Jani Onninen, Xiao Zhong (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.
K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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Devdariani, G. (2000)
Bulletin of TICMI
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Nazarov, A.I. (2004)
Journal of Mathematical Sciences (New York)
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Joseph H. Silverman (2012)
Acta Arithmetica
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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.
Grzegorz Łysik, Paweł M. Wójcicki (2014)
Annales Polonici Mathematici
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We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.
B. Szafirski (1967)
Colloquium Mathematicae
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Tiantian Qiao, Weiguo Li, Kai Liu, Boying Wu (2014)
Annales Polonici Mathematici
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The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.
Nestke, A., Zickermann, F.
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Joseph H. Silverman, Katherine E. Stange (2011)
Acta Arithmetica
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Chun Li, Zeng-Qi Ou, Chun-Lei Tang (2013)
Studia Mathematica
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Using a version of the Local Linking Theorem and the Fountain Theorem, we obtain some existence and multiplicity results for a class of superquadratic elliptic equations.
Flavia Giannetti
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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.
Henryk Kołakowski, Jarosław Łazuka (2008)
Applicationes Mathematicae
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The aim of this paper is to derive a formula for the solution to the Cauchy problem for the linear system of partial differential equations describing nonsimple thermoelasticity. Some properties of the solution are also presented. It is a first step to study the nonlinear case.
N. Tzanakis (2002)
Acta Arithmetica
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