Functional-differential equations with compressed arguments and polynomial coefficients: Asymptotics of the solutions
The functional-differential equation with linearly compressed arguments and polynomial coefficients \(y^{(m)}(t)=\sum^l_{j=0}\sum^{m-1}_{k=0}\sum^r_{\nu=0}a_{jk\nu}t^\nu y^{(k)}(\alpha_jt)\) is considered. Under some restrictions it is proved that each solution \(y(t)\) of this equation, satisfying the estimate \(|y(t)|<C\text{exp}\{\gamma\ln^2(1+|t|)\}\), \(t\in\mathbb{R}_+\), where \(0<\gamma<\widetilde\gamma\), is a polynomial.
scientific article; zbMATH DE number 811197