A note on bounded solutions of second order differential equations at resonance

Wioletta Karpińska

DOI: http://dx.doi.org/10.12775/TMNA.1999.040

Abstract


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.

Keywords


Differential equations; resonance; boundedness; unbounded domain

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