Twopoint nonlocal problem for a weak nonlinear differential operator equation 

Author 
i.volyanska@i.ua^{1}, ilkivv@i.ua^{2}, n.strap@i.ua^{3}
1) Lviv Polytechnic National University, Lviv, Ukraine; 2) Lviv Polytechnic National University, Lviv, Ukraine; 3) College of Oil and Gas, Drohobych, Lviv region, Ukraine

Abstract 
In the paper is have studied the solvability of a twopoint nonlocal boundaryvalue problem
for the operatordifferential equation with weakly nonlinear righthand side. The proof of the
theorems is carried out within the Nash–Moser iterative scheme. In this scheme, the important
point is the construction of estimates to the norms of inverse linearized operators arising at
each step of this scheme and by the related problem of small denominators. The inverse of
linearized operators is obtained by the method developed in the work of M. Berti, P. Bolle
(Duke Math. J., 134 (2), 359–419 (2006)). The problem of small denominators is solved by
using the metric approach.

Keywords 
nonlocal problem; small denominators; metric estimation; Nash–Moser iterative scheme

DOI 
doi:10.15330/ms.50.1.4459

Reference 
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Pages 
4459

Volume 
50

Issue 
1

Year 
2018

Journal 
Matematychni Studii

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