On the $psi$-dichotomy for homogeneous linear differential equations

Abstract

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 $x'=A(t)x +f(t)$ has at least one $psi$-bounded solution on $(0,+infty)$.

Keywords

• $psi$-bounded
• $psi$-integrable
• $psi$-integrally bounded
• $psi$-exponential.