Abstract
In the paper we study the existence of bounded solutions for differential equations of the form: $x''-Ax= f(t,x)$, where $A\in L(H)$, $f\colon {\mathbb R}\times H \to H$ ($H$ - 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.
Citation
Wioletta Karpińska. "A note on bounded solutions of second order differential equations at resonance." Topol. Methods Nonlinear Anal. 14 (2) 371 - 384, 1999.
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