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Inclusion statements for operator equations by a continuity principle (1977)

Schröder, Johann

Springer

Manuscripta mathematica 21 (1977), S. 135-171

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ISSN: 1432-1785

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The paper is concerned with Range-Domain Implications Mv∈C⇒v∈K, where M is a given operator and C,K denote given sets. Sufficient conditions are derived by a very general continuity principle. Various special cases are considered such as inverse-positivity, Mv≤Mw⇒v≤w, and a generalization H(ϕ,[ϕ,ψ])≤Mv≤H(ψ,[ϕ,ψ]) ⇒ϕ≤v≤ψ, where Mu=H(u,u) and [ϕ,ψ] denotes an order interval. These results are applied to differential operators related to boundary or initial value problems. The goal is to furnish a simple uniform approach, to explain its application, and to provide a kind of survey on what problems have been treated in this way.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01168016

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