An asymptotic formula for solutions of nonoscillatory half-linear differential equations

Ondřej Došlý and Jana Řezníčková

Address:
Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
Department of Mathematics, Tomas Bata University, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic

E-mail:
dosly@math.muni.cz
reznickova@fai.utb.cz

Abstract: We establish a Hartman type asymptotic formula for nonoscillatory solutions of the half-linear second order differential equation \[ \left(r(t)\Phi (y^{\prime })\right)^{\prime }+c(t)\Phi (y)=0\,,\quad \Phi (y):=|y|^{p-2}y\,,\ p>1\,. \]

AMSclassification: primary 34C10.

Keywords: half-linear differential equation, asymptotic formula, principal solution.