and recall some basic facts of maximal monotone relations. Section 3 is devoted to the well-posedness result for inclusions of the form in an exponentially weighted $L_{2}$-space. In Section 4 we prove under stronger assumptions the causality of the solution operator and its independence of the particular choice of the exponential weight (see for the precise statement). Finally, we apply our results to a semistatic quasilinear variant of Maxwell’s equations and thereby generalise the result of [@Milani_Picard1995].

Preliminaries
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We begin by introducing the Hilbert space setting we are working with throughout this article. Throughout let $H$ denote a Hilbert space (real or complex, in case of a real Hilbert space one can ignore all forthcoming occurring real parts) with inner product $\langle\cdot,\cdot\rangle$ and induced norm $|\cdot|.$ Following [@Picard_McGhee; @Picard] we introduce the following weighted $L_{2}$-space and the derivative operator defined on it.

Let $\rho\geq0.$ We define the following space of (equivalence classes of) square integrable functions with respect to an exponentially weighted Lebesgue measure $$L_{2,\rho}({\mathbb{R}};H)\coloneqq\left\{ f:{\mathbb{R}}\to H\,;\,f\text{ Bochner-measurable, }\intop_{{\mathbb{R}}}|f(t)|^{2}\,{\mathrm{e}}^{-2\rho t}{\,\mathrm{d}}t<\infty\right\} .$$ Clearly, $L_{2,\rho}({\mathbb{R}};H)$ becomes a Hilbert space equipped with the usual inner product $$\langle f,g\rangle_{\rho}\coloneqq\intop_{{\mathbb{R}}}\langle f(t),g(t)\rangle\,{\mathrm{e}}^{-2\rho t}{\,\mathrm{d}}t\quad(f,g\in L_{2,\rho}({\mathbb{R}};H)).$$ We denote the induced norm by $|\cdot|_{\rho}.$ Moreover, we define the 