Nonoscillatory solutions of half-linear Euler-type equation with n terms

Abstract

We consider the half-linear Euler-type equation with n terms (Phi(x '))'+(gamma(p)/t(p) + Sigma(n-1)(j=1) mu(p)/t(p)Log(j)(2)t +mu/t(p)Log(n)(2)t)Phi(x)=0, Phi(x)=|x|(p-1)sgnx in the subcritical case when 0<mu<mu(p) 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.