Two-point nonlocal problem for a weak nonlinear differential operator equation
Journal Title: Математичні Студії - Year 2018, Vol 50, Issue 1
Abstract
In the paper is have studied the solvability of a two-point nonlocal boundary-value problem for the operator-differential equation with weakly nonlinear right-hand 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.
Authors and Affiliations
I. Volyanska, V. Il’kiv, N. Strap
Keywords
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- EP ID EP436194
- DOI 10.15330/ms.50.1.44-59
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