On the $psi$-dichotomy for homogeneous linear differential equations
In this article we present some conditions for the $psi$-dichotomy of the homogeneous linear differential equation $x'=A(t)x$. Under our condition every $psi$-integrally bounded function $f$ the nonhomogeneous linear differential equation $x'=A(t)x ...
Pham Ngoc Boi
doaj
Existence of $psi$-bounded solutions for nonhomogeneous linear differential equations
In this article we present a necessary and sufficient condition for the existence of $psi$-bounded solution on $mathbb{R}$ of the nonhomogeneous linear differential equation $x'=A(t)x+f(t)$.
Pham Ngoc Boi
doaj
Summary: In this paper we give a characterization for the existence of \(\Psi\)-bounded solutions on \(\mathbb{R}\) for the system \[ x'=A(t)x + f(t), \] assuming that f is a Lebesgue \(\Psi\)-integrable function on \(\mathbb{R}\). In addition, we give a result in connection with the asymptotic behavior of the \(\Psi\)-bounded solutions of this system.
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