Existence of solutions of nonlinear differential equations with $\psi$-exponential or $\psi$-ordinary dichotomous linear part in a Banach space

• Main Authors: Atanaska Georgieva, Hristo Kiskinov, Stepan Kostadinov, Andrey Zahariev
• Format: Article
• Language: English
• Published: University of Szeged 2014-03-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: $\psi$-dichotomy for ordinary differential equations; $\psi$-boundedness.
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=2554
• ISSN: 1417-3875; 1417-3875

In this article we consider nonlinear differential equations with $\psi$-exponential and $\psi$-ordinary dichotomous linear part in a Banach space. By the help of the fixed point principle of Banach sufficient conditions are found for the existence of $\psi$-bounded solutions of these equations on $\mathbb{R}$ and $\mathbb{R}_+$.