Bounded solutions of weakly nonlinear differential equations in a Banach space

Bounded solutions of weakly nonlinear differential equations in a Banach space

For a weakly nonlinear differential equation in a Banach space, we establish necessary and sufficient conditions for the existence of solutions bounded on the entire real axis under the assumption that the generating equation has bounded solutions and the corresponding homogeneous equation admits an...

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Veröffentlicht in:Nonlinear oscillations 2008-04, Vol.11 (2), p.158-167
Hauptverfasser: Boichuk, O. A., Pokutnyi, O. O.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Zusammenfassung:For a weakly nonlinear differential equation in a Banach space, we establish necessary and sufficient conditions for the existence of solutions bounded on the entire real axis under the assumption that the generating equation has bounded solutions and the corresponding homogeneous equation admits an exponential dichotomy on the semiaxes.
ISSN:1536-0059
1536-0059
DOI:10.1007/s11072-008-0021-9