On a conjecture of R. Brück and some linear differential equations

In this paper, we mainly investigate the Brück conjecture concerning entire function f and its differential polynomial L 1 ( f ) = a k ( z ) f ( k ) + ⋯ + a 0 ( z ) f sharing an entire function α ( z ) with σ ( α ) ≤ σ ( f ) , by using the theory of complex differential equation.Mathematics Subject Classification: 39B32, 30D 35.

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