De Haan type increasing solutions of half-linear differential equations

We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation (r(t)|y′|α−1sgny′)′=p(t)|y|α−1sgny, where r,p are positive continuous functions and α∈(1,∞). We give conditions which guarantee that any such a solution is in the class Γ (in the de Haan sense). We also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts. The results can be viewed as a half-linear extension of existing statements for linear equations, but in some aspects they are new also in the linear case.