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Oscillatory solutions of nonhomogeneous linear differential equations. (English) Zbl 0870.34003
Summary: The complex oscillation of nonhomogeneous linear differential equations with transcendental coefficients is discussed. Results concerning the equation \(f^{(k)} +a_{k-1} f^{(k-1)} +\cdots +a_\wedge f=F\) where \(a_\wedge, \dots, a_{k-1}\) and \(F\) are 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 \(a_1,\dots,a_{k-1}\) are polynomials and \(F= h\exp(p_0)\), where \(p_0\) is a polynomial and \(h\) is an entire function.

MSC:
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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