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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.
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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