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Nonoscillatory solutions of half‐linear Euler‐type equation with n terms
Author(s) -
Pátíková Zuzana
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5930
Subject(s) - mathematics , riccati equation , type (biology) , euler's formula , mathematical analysis , euler equations , fixed point theorem , pure mathematics , differential equation , ecology , biology
We consider the half‐linear Euler‐type equation with n terms( Φ ( x ′ ) ) ′ +γ pt p+∑ j = 1 n − 1μ pt pLog j 2 t + μt pLog n 2 tΦ ( x ) = 0 , Φ ( x ) = | x | p − 1 sgn x in the subcritical case when 0< μ < μ 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.