## On the growth of solutions of a class of higher order linear differential equations with extremal coefficients.(English)Zbl 1476.34181

Summary: We consider that the linear differential equations $f^{(k)} + A_{k - 1}(z) f^{(k - 1)} + \cdots + A_1(z) f' + A_0(z) f = 0\,,$ where $$A_j (j = 0,1, \dots, k - 1)$$, are entire functions. Assume that there exists $$l \in \{1,2, \dots, k - 1 \}$$, such that $$A_l$$ is extremal for Yang’s inequality; then we will give some conditions on other coefficients which can guarantee that every solution $$f(\not\equiv 0)$$ of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of $$f$$ if every solution $$f(\not\equiv 0)$$ of the equation is of infinite order.

### MSC:

 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 34M03 Linear ordinary differential equations and systems in the complex domain

### Keywords:

every solution; infinite order; lower bound of hyperorder
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### References:

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