MMN-1983

# On conversion of resonant problem to non-resonant one

**N. Sveikate**, Daugavpils University, Department of Mathematics, Parades str. 1, LV-5401 Daugavpils, Latvia,`nsveikate@inbox.lv`

**F. Sadyrbaev**, Institute of Mathematics, University of Latvia, Rainis boul. 29, LV-1459 Riga, Latvia,`felix@latnet.lv`

## Abstract

We consider a nonlinear resonant boundary value problem. To prove
the existence of a solution to a given boundary value problem we
replace the linear part of a given equation by non-resonant linear
part. First, to modify a resonant problem to a regular one we use
the Taylor expansion for $f(t,x)$ with respect to $x$. The second
way of conversion a given problem to non-resonant one is based on
an appropriate choice of ``good" approximation to expected
solution. We provide the existence results illustrating both ways.

Vol. 18 (2017), No. 2, pp. 1059-1071

DOI: 10.18514/MMN.2017.1983