Solutions of half-linear differential equations in the classes Gamma and Pi. (English) Zbl 1374.34206

Řehák, Pavel; Taddei, Valentina

Differ. Integral Equ. 29, No. 7-8, 683-714 (2016).

The authors study the asymptotic behavior of solutions of the differential equation \[ (r(t)\Phi(y'))'=p(t)\Phi(y), \] where \(r\) and \(p\) are positive continuous functions and \(\Phi(u)=|u|^{\alpha -1}\operatorname{sgn}u\) with \(\alpha>1\). They find conditions under which the solutions belong to the so-called Haan classes.

Reviewer: Sergei Yu. Pilyugin (St. Petersburg)

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34C11	Growth and boundedness of solutions to ordinary differential equations
26A12	Rate of growth of functions, orders of infinity, slowly varying functions

Keywords:

semilinear differential equations; asymptotic behavior of solutions; de Haan class