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MULTIPLE SOLUTIONS FOR A NONHOMOGENEOUS SCHRODINGER-POISSON SYSTEM WITH CONCAVE AND CONVEX NONLINEARITIES
Li xia Wang
Keywords:Schr\"{o}dinger-Poisson systems; concave and convex nonlinearities; variational methods; Ekeland's variational principle; Mountain Pass Theorem
Abstract:
      In this paper, we consider the following nonhomogeneous Schr\"{o}dinger-Poisson equation \begin{align*} (*) \begin{cases} - \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\-\Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3, \\end{cases} \end{align*} where $1