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摘要
Consider the following Schrodinger-Poisson-Slater system, where omega > 0, lambda > 0 and beta > 0 are real numbers, p a (1, 2). For beta = 0, it is known that problem (P) has no nontrivial solution if lambda > 0 suitably large. When beta > 0, -beta/|x| is an important potential in physics, which is called external Coulomb potential. In this paper, we find that (P) with beta > 0 has totally different properties from that of beta = 0. For beta > 0, we prove that (P) has a ground state and multiple solutions if lambda > c (p,omega) , where c (p,omega) > 0 is a constant which can be expressed explicitly via omega and p.
- 出版日期2014-6
- 单位中南财经政法大学; 中国科学院武汉物理与数学研究所
