LAUSR

Using the data sample of an integrated luminosity of 2.93 fb$^{-1}$ taken at the center-of-mass energy of 3.773 GeV, we search for the Majorana neutrino in the lepton number violating decays $D\to K \pi e^+ e^+$. No significant signal is observed, and the upper limits on the branching fraction at the 90\% confidence level are set to be $\mathcal{B}\,(D^0 \to K^- \pi^- e^+ e^+)<2.7\times10^{-6}$, $\mathcal{B}\,(D^+ \to K_S^0 \pi^- e^+ e^+)<3.3\times10^{-6}$ and $\mathcal{B}\,(D^+ \to K^- \pi^0 e^+ e^+)<8.5\times10^{-6}$. The Majorana neutrino is searched for with different mass assumptions ranging from 0.25 to 1.0 GeV/$c^2$ in the decays $D^0\to K^- e^+ \nu_N(\pi^- e^+)$ and $D^+\to K_S^0 e^+ \nu_N(\pi^- e^+)$, and the upper limits on the branching fraction at the 90\% confidence level are extracted to be at the level of $10^{-7} \sim 10^{-6}$, depending on the mass of Majorana neutrino. The constraints on the mixing matrix element $|V_{eN}|^2$ are also evaluated.