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We establish a Hartman type asymptotic formula for nonoscillatory solutions of the half-linear second order differential equation $${\left(r\left(t\right)\Phi \left(y^{\text{'}}\right)\right)}^{\text{'}}+c\left(t\right)\Phi \left(y\right)=0,\Phi \left(y\right):={\left|y\right|}^{p-2}y,p>1.$$

We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation $${\left(r\left(t\right)\Phi \left(x^{\text{'}}\right)\right)}^{\text{'}}+c\left(t\right)\Phi \left(x\right)=0,\Phi \left(x\right):={\left|x\right|}^{p-2}x,p>1(*)$$ and we show that if (*) is regular, a solution $x$ of this equation such that $x^{\text{'}}\left(t\right)\ne 0$ for large $t$ is principal if and only if $${\int }^{\infty }\frac{dt}{r\left(t\right)x^2\left(t\right){\left|x^{\text{'}}\left(t\right)\right|}^{p-2}}=\infty .$$ Conditions on the functions $r,c$ are given which guarantee that (*) is regular.