Simple zeros of solutions of $n\textrm {th}$-order linear differential equations

Abstract:

Let the $n$th-order linear differential equation $Ly = 0$ have a nontrivial solution with $n$ zeros (counting multiplicities) on an interval $[\alpha ,\beta ]$. A condition under which $Ly = 0$ has a solution with $n$ simple zeros on $[\alpha ,\beta ]$ is established. Also, a new proof is given for a known result concerning an interval of the type $[\alpha ,\beta )$.