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.
Chang-Shou Lin (1994)
Manuscripta mathematica
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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.
Qun Lin, Hehu Xie, Fei Xu (2015)
Applications of Mathematics
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A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated...
Chi-ping Lau (1987)
Manuscripta mathematica
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Gabriella Tarantello, Stanley Alama (1996)
Mathematische Zeitschrift
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Jens Frehse (1979)
Manuscripta mathematica
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Mario Zuluaga Uribe (2001)
Archivum Mathematicum
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In this paper we consider the existence of nonzero solutions of an undecoupling elliptic system with zero Dirichlet condition. We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions and we give applications to biharmonic equations and the scalar case.
K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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