Geodesic
Poisson Stable Solutions of Semi-Linear Differential Equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2024), pp. 17-43

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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. 
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     title = {Poisson {Stable} {Solutions} of {Semi-Linear} {Differential} {Equations}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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David Cheban. Poisson Stable Solutions of Semi-Linear Differential Equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2024), pp. 17-43. http://geodesic.mathdoc.fr/item/BASM_2024_1_a2/