On the Complex Oscillation of Some Linear Differential Equations

We treat the linear differential equation ). f k.qA z.fs0, where kP2 is an integer and A z. is a transcendental entire function of order s A.. It is shown that any non-trivial solution of the equation ). satisfies l f.Ps A., where l f. is the exponent of convergence of the zero-sequence of f, under the condition KN r, 1rA.OT r, A., rfE for a K)2k and an exceptional set E of finite linear measure. The second order equation f 0 q e P1 z .qe P2 z .qQ z..fs0, where P1 z., P2 z. are non-constant polynomials and Q z. is an entire function, is also studied