Oscillatory solutions of nonhomogeneous linear differential equations

The complex oscillation of nonhomogeneous linear differential equations with transcendental coefficients is discussed. Results concerning the equation f ^(k)+a _k−1 f ^(k−1)+...+a ₀ f=F where a ₀,...,a _k−i and Fare entire functions, possessing an oscillatory solution subspace in which all solutions (with at most one exception) have infinite exponent of convergence of zeros are obtained. All solutions of the equation are also characterized when the coefficients a ₀,a ₁,...,a _k−1 are polynomials and F=h exp (p ₀), where p ₀ is a polynomial and h is an entire function. Author supported by Max-Planck-Gesellschaft and by NSFC.