On the eigenvalue problem of Schr\"{o}dinger-Poisson system.

In this paper, we are concerned with the following Schrödinger-Poisson system with nonhomogeneous boundary conditions \begin{equation*} \begin {cases} -\frac {1}{2}\triangle {u}+\phi u =\omega u, & \text {in }\Omega, \\ -\triangle {\phi }=4\pi u^2, & \text {in } \Omega,\\ \phi =h,u=0, & \text {on } \partial \Omega, \end{cases} \end{equation*} where \Omega is a smooth and bounded domain in \mathbb {R}^3, h is a given nonnegative regular function on \partial \Omega and \omega \in \mathbb {R}. By using variational method and bifurcation theory, we obtain the existence of positive solutions to the above system for \omega larger than some positive constant. [ABSTRACT FROM AUTHOR]