Constructive analysis of periodic solutions with interval halving
Result description
For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution. An interval halving technique is introduced by using which one can weaken significantly the conditions required to guarantee the convergence. The main assumption on the equation is that the non-linearity is locally Lipschitzian. An existence theorem based on properties of approximations is proved. A relation to Mawhin's continuation theorem is indicated.
Keywords
periodic successive approximationsnumerical-analytic methodMawhin's theorem
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Constructive analysis of periodic solutions with interval halving
Original language description
For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution. An interval halving technique is introduced by using which one can weaken significantly the conditions required to guarantee the convergence. The main assumption on the equation is that the non-linearity is locally Lipschitzian. An existence theorem based on properties of approximations is proved. A relation to Mawhin's continuation theorem is indicated.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Boundary value problems
ISSN
1687-2770
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
22 March
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
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UT code for WoS article
000325724300001
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2013