Differential equations of the form \(f'' + A(z)f' + B(z)f = 0\) (*) are considered, where A(z) and \(B(z) \not \equiv 0\) are entire functions. The Lindelöf function is used to show that for any \(\rho \in (1/2, \infty )\), there exists an equation of the form (*) which possesses a solution f with a Nevanlinna deficient value at 0 satisfying \(\rho =\rho (f)\ge \rho (A)\ge \rho (B)\), where \(\rho (h)\) denotes the order of an entire function h. It is known that such an example cannot exist when \(\rho \le 1/2\). For smaller growth functions, a geometrical modification of an example of Anderson and Clunie is used to show that for any \(\rho \in (2, \infty )\), there exists an equation of the form (*) which possesses a solution f with a Valiron deficient value at 0 satisfying \(\rho =\rho _{\log }(f)\ge \rho _{\log }(A)\ge \rho _{\log }(B)\), where \(\rho _{\log }(h)\) denotes the logarithmic order of an entire function h. This result is essentially sharp. In both proofs, the separation of the zeros of the indicated solution plays a key role. Observations on the deficient values of solutions of linear differential equations are also given, which include a discussion of Wittich’s theorem on Nevanlinna deficient values, a modified Wittich theorem for Valiron deficient values, consequences of Gol’dberg’s theorem, and examples to illustrate possibilities that can occur.

考虑形式为\（f''+ A（z）f'+ B（z）f = 0 \）（*）的微分方程，其中A（z）和\（B（z）\ not \ equiv 0 \）是全部功能。Lindelöf函数用于表明，对于任何\（\ rho \ in（1/2，\ infty）\），存在一个形式为（*）的方程，该方程具有n为零的Nevanlinna不足值的解f满足\（\ rho = \ rho（f）\ ge \ rho（A）\ ge \ rho（B）\），其中\（\ rho（h）\）表示整个函数h的阶数。众所周知，当\（\ rho \ le 1/2 \）时，这样的示例将不存在。对于较小的增长函数，对Anderson和Clunie的示例进行了几何修改，以显示对于任何\（\ rho \ in（2，\ infty）\），存在一个形式为（*）的方程，该方程具有解决方案f的Valiron不足值为0满足\（\ rho = \ rho _ {\ log}（f）\ ge \ rho _ {\ log}（A）\ ge \ rho _ {\ log}（B）\ ），其中\（\ rho _ {\ log}（h）\）表示整个函数h的对数阶。该结果实质上是清晰的。在这两种证明中，指示解的零点的分离起着关键作用。还给出了对线性微分方程解解的不足值的观察，包括对Nevanlinna不足值的Wittich定理的讨论，对Valiron不足值的修改的Wittich定理，Gol'dberg定理的结果以及举例说明可以发生。