Asymptotic behavior of solutions of a nonlinear difference equation with continuous argument

• Datum: 2004
• Hauptverfasser: Stevic, S., Штевич, С.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2004
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3824
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We consider the difference equation with continuous argument $$x(t + 2) - 2\lambda x(t + 1) + \lambda ^2 x(t) = f(t,x(t)),$$ where λ > 0, t ∈ [0, ∞), and f: [0, ∞) × R → R. Conditions for the existence and uniqueness of continuous asymptotically periodic solutions of this equation are giv...