@article{Karpińska_1999, title={A note on bounded solutions of second order differential equations at resonance}, volume={14}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.1999.040}, abstractNote={In the paper we study the existence of bounded solutions for differential
equations of the form:
$ x’’-Ax= f(t,x)$, where $A\in L(H)$, $f: {\mathbb R}\times H \to H$
($H$ -- a Hilbert space) is a continuous mapping.
Using a perturbation of the equation, the Leray-Schauder topological degree
and fixed point theory, we overcome the difficulty that the linear problem is non-Fredholm in any resonable Banach space.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Karpińska, Wioletta}, year={1999}, month={Dec.}, pages={371–384} }