On conversion of resonant problem to non-resonant one
- N. Sveikate,
Daugavpils University, Department of Mathematics, Parades str. 1, LV-5401 Daugavpils, Latvia,
- F. Sadyrbaev,
Institute of Mathematics, University of Latvia, Rainis boul. 29, LV-1459 Riga, Latvia,
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