Journal
ARCHIV DER MATHEMATIK
Volume 82, Issue 5, Pages 442-448Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00013-003-4796-8
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In this paper, we shall utilize Nevanlinna value distribution theory to study the solvability of transcendental meromorphic function f(z) that satisfies the differential equations of the form: f(2)(z) + b(z)(L(f))(2) = a(z), where L(f) denotes a linear differential polynomial in f, a (z) and b(z) are nonzero small functions of f(z). As an application, the method developed here can be used, for instance, to obtain all the entire solutions of the nonlinear differential equation 4 f(3) (z) + 3 f (z) = - sin 3z.
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