| Abstract: | Summary In this paper some properties of solutions of the differential equation Y″(t)++P(t) Y(t)=0 in Banach spaces are investigated.
In particular, conditions are given for some solutions of such equations to possess an infinite number of zeros as t → ∞ while
another condition ensures some solutions possess only a finite number of zeros, Some examples and a theorem show the concept
of an oscillatory solution of a differential equation in a Banach space involves pathologies not found in the case of finite
dimensional spaces. Upon specialization of the Banach spaces involved the results reduce to known theorems.
Entrata in Redazione il 13 maggio 1969. |
