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Differential polynomials generated by second order linear differential equations. (English) Zbl 1165.34430
Summary: We study fixed points of solutions of the differential equation
$f^{{\prime \prime }}+A_{1}( z) f^{{\prime }}+A_{0}(z) f=0,$ where $$A_{j}(z) ( \not\equiv 0)$$, $$j=0, 1$$, are transcendental meromorphic functions with finite order. Instead of looking at the zeros of $$f( z)-z$$, we proceed to a slight generalization by considering zeros of $$g(z)-\varphi ( z)$$, where $$g$$ is a differential polynomial in $$f$$ with polynomial coefficients, $$\varphi$$ is a small meromorphic function relative to $$f$$, while the solution $$f$$ is of infinite order.
MSC:
 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
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