Application of p-regularity theory to the Duffing equation

The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , where F : C 2 [ 0 , 2 π ] × R × R → C [ 0 , 2 π ] and x ( 0 ) = x ( 2 π ) = 0 using the p -regularity theory.

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Veröffentlicht in:	Boundary value problems 2017-06, Vol.2017 (1), p.1-9, Article 85
Hauptverfasser:	Medak, Beata, Tret’yakov, Alexey A
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximations and Expansions Difference and Functional Equations Duffing equation Mathematics Mathematics and Statistics nonlinear boundary value problems Nonlinearity Ordinary Differential Equations p-factor operator p-regularity Partial Differential Equations Regularity
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Beschreibung
Zusammenfassung:	The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , where F : C 2 [ 0 , 2 π ] × R × R → C [ 0 , 2 π ] and x ( 0 ) = x ( 2 π ) = 0 using the p -regularity theory.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-017-0815-8