Behavior at infinity of psi-evanescent solutions to linear differential equations

Abstract

In this article we present some necessary and sufficient conditions for the existence of $psi$-evanescent solution of the nonhomogeneous linear differential equation $x'=A(t)x+f(t)$, which is related to the notion of $psi$-ordinary dichotomy for the equation $x'=A(t)x$. We associate that with the condition of $psi$-ordinary dichotomy for the homogeneous linear differential equation $x'=A(t)x$.

Keywords

• psi-bounded solutions
• psi-ordinary dichotomy
• psi-evanescent solutions