Stability of Bounded Solutions of Differential Equations with Small Parameter in a Banach Space

• Datum: 2003
• Hauptverfasser: Gorodnii, M. F., Городній, М. Ф.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2003
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3964
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

For a sectorial operator A with spectrum σ(A) that acts in a complex Banach space B, we prove that the condition σ(A) ∩ i R = Ø is sufficient for the differential equation \(\varepsilon x_\varepsilon^\prime\prime(t)+x_\varepsilon^\prime(t)=Ax_\varepsilon(t)+f(t), t \in R,\) where ε is a small po...