I am looking for a reference to the following problem: Given a hyperbolic (no purely imaginary eigenvalues), continuous path of matrices $A(t)$ in $\mathbb{R}$ with hyperolic limits at $\pm \infty $. Under which assumptions (on A(t)) is the operator $F_A :=\frac{d}{dt} +A(t) :H^1 (\mathbb{R},\mathbb{R}^m )\to L^2 (\mathbb{R},\mathbb{R}^m )$ injective, resp. surjective?
Injectivity/Surjectivity of $F_A :=\frac{d}{dt} +A(t) :H^1 (\mathbb{R},\mathbb{R}^m )\to L^2 (\mathbb{R},\mathbb{R}^m )$
Florian Zeiser
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