The Set of Solutions of the Dirichlet Problem between Lower and Upper Functions Is Connected

The Set of Solutions of the Dirichlet Problem between Lower and Upper Functions Is Connected

Under appropriate conditions, we prove that for two arbitrary solutions and of the Dirichlet problem lying between lower and upper functions there exists a continuous mapping of the interval into the solution set of the Dirichlet problem such that and .

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Veröffentlicht in:Differential equations 2020-05, Vol.56 (5), p.676-678
1. Verfasser: Lepin, A. Ya
Format: Artikel
Sprache:eng
Schlagworte:
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Physical Sciences
Science & Technology
Short Communications
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Beschreibung
Zusammenfassung:Under appropriate conditions, we prove that for two arbitrary solutions and of the Dirichlet problem lying between lower and upper functions there exists a continuous mapping of the interval into the solution set of the Dirichlet problem such that and .
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266120050134