Integral conditions for right disfocality of a linear differential equation (Q1109191)

The authors consider the nth order linear differential equation (1) \(y^{(n)}+\sum^{n}_{i=1}p_ i(t)y^{(n-i)}=0.\) The equation (1) is right disfocal on an interval I, if the only solution of (1) satisfying \(y^{(i-1)}(t_ i)=0\), \(1\leq i\leq n\), where \(t_ 1\leq...\leq t_ n\) belong to I, is the trivial solution. The main result is Theorem 2.5: Assume that \(p_ 1,...,p_ n\in C[0,\infty)\) satisfy \(\int^{\infty}t^{k-1}| p_ k(t)| dt<\infty,\) \(1\leq k\leq n\). Then there exists \(a>0\) such that (1) is right disfocal on [a,\(\infty)\).