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We consider the half‐linear Euler‐type equation with n terms (Φ(x′))′+γptp+∑j=1n−1μptpLogj2t+μtpLogn2tΦ(x)=0,Φ(x)=|x|p−1sgnxin the subcritical case when 0<μ<μp and p>1. The solutions of this nonoscillatory equation cannot be found in an explicit form and can be studied only asymptotically. In this paper, with the use of the perturbation principle, modified Riccati technique, and the fixed point theorem, we establish an asymptotic formula for one of its solutions. [ABSTRACT FROM AUTHOR]

We establish new oscillation and nonoscillation criteria for the perturbed generalized Riemann-Weber half-linear equation with critical coefficients. (Φ(x'))' + (γp/tp + nΣ j=1 μp/tpLogj2t + c(t)) Φ (c) = 0 in terms of the expression 1/logn+1t ƒt c(s) sp-1 Lognslogn+12s ds. [ABSTRACT FROM AUTHOR]

Abstract: We establish asymptotic formulas for non-oscillatory solutions of the half-linear second-order differential equation where this equation is viewed as a perturbation of the half-linear Euler equation. [Copyright &y& Elsevier]

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation). [ABSTRACT FROM AUTHOR]