Orders of Solutions of an n-th Order Linear Differential Equation with Entire Coefficients
Southwest Texas State University, Department of Mathematics
We study the solutions of the differential equation f(n) + An-1(z) ƒ(n-1) + ∙∙∙ + A1(z) ƒ' + A0(z) ƒ = 0, where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.
Linear differential equations, Entire functions, Order of growth
Belaidi, B., & Hamouda, S. (2001). Orders of solutions of an n-th order linear differential equation with entire coefficients. <i>Electronic Journal of Differential Equations, 2001</i>(61), pp. 1-5.