Poisson Stable Solutions of Semi-Linear Differential Equations

David Cheban

State University of Moldova, Faculty of Mathematics and Computer Science, Laboratory of Fundamental and Applied Mathematics, A. Mateevich Street 60, MD–2009 Chişinău, Moldova

Аннотация: We study the problem of existence of Poisson stable (in particular, almost periodic, almost automorphic, recurrent) solutions to the semi-linear differential equation
$$ x'=(A_0+A(t))x+F(t,x) $$
with unbounded closed linear operator $A_0$, bounded operators $A(t)$ and Poisson stable functions $A(t)$ and $F(t,x)$. Under some conditions we prove that there exists a unique (at least one) solution which possesses the same recurrence property as the coefficients.

Ключевые слова и фразы: poisson stable motions, linear nonautonomous dynamical systems, semi-linear differential equations.

MSC: 34D09, 34D10, 35B10, 35B15, 35B20

Поступила в редакцию: 10.01.2024

Язык публикации: английский

DOI: 10.56415/basm.y2024.i1-2.p17