TY - JOUR
AU - KarpiĆska, Wioletta
PY - 1999/12/01
Y2 - 2023/03/27
TI - A note on bounded solutions of second order differential equations at resonance
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 14
IS - 2
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.1999.040
SP - 371 - 384
AB - In the paper we study the existence of bounded solutions for differentialequations 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 degreeand fixed point theory, we overcome the difficulty that the linear problem is non-Fredholm in any resonable Banach space.
ER -