  This paper deals with a complex third order linear measure differential
equation \begin{equation*} i\mathrm{d}\left( y^{\prime }\right) ^{\bullet
}+2iq\left( x\right) y^{\prime }\mathrm{d}x+y\left( i\mathrm{d}q\left( x\right)
+\mathrm{d}p\left( x\right) \right) = \lambda y\mathrm{d}x \end{equation*} on a
bounded interval with boundary conditions presenting a mixed aspect of the
Dirichlet and the periodic problems. The dependence of eigenvalues on the
coefficients $p$, $q$ is investigated. We prove that the $n$-th eigenvalue is
continuous in $p$, $q$ when the norm topology of total variation and the
weak$^*$ topology are considered. Moreover, the Fr\'{e}chet differentiability
of the $n$-th eigenvalue in $p$, $q$ with the norm topology of total variation
is also considered. To deduce these conclusions, we investigate the dependence
of solutions of the above equation on the coefficients $p$, $q$ with different
topologies and establish the counting lemma of eigenvalues according to the
estimates of solutions.
