Existence of $psi$-bounded solutions for a system of differential equations

Abstract

In this article, we present a necessary and sufficient condition for the existence of solutions to the linear nonhomogeneous system $x'=A(t)x + f(t)$. Under the condition stated, for every Lebesgue $Psi$-integrable function $f$ there is at least one $Psi$-bounded solution on the interval $(0,+infty)$.

Keywords

• $Psi$-bounded
• Lebesgue $Psi$-integrable function.