Albo Carlos Cavalheiro (2017)
Communications in Mathematics
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The main result establishes that a weak solution of degenerate semilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate semilinear elliptic equations.
K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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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.
Devdariani, G. (2000)
Bulletin of TICMI
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Nazarov, A.I. (2004)
Journal of Mathematical Sciences (New York)
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Gabriella Tarantello, Stanley Alama (1996)
Mathematische Zeitschrift
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Joseph H. Silverman (2012)
Acta Arithmetica
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Fei Xu, Hehu Xie (2017)
Applications of Mathematics
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A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also...
Bochev, P., Gunzburger, M. (2004)
Zapiski Nauchnykh Seminarov POMI
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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.
Joseph H. Silverman, Katherine E. Stange (2011)
Acta Arithmetica
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