Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 86, pp. 1-19.

Title: Multiple positive solutions for Schrodinger-Poisson systems
       involving concave-convex nonlinearities

Author: Haining Fan (China Univ. of Mining and Technology, Xuzhou, China)

Abstract:
 In this article, we study the existence of multiple positive solutions
 for Schrodinger-Poisson systems involving concave-convex nonlinearities
 and sign-changing weight potentials. With the help of Nehari manifold
 and Ljusternik-Schnirelmann category theory, we investigate how the coefficient
 g(x) of the critical nonlinearity  affects the number of positive solutions.
 Furthermore, we obtain a relationship between the number of positive solutions
 and the topology of the global maximum set of g.

Submitted July 24, 2018. Published July 16, 2019.
Math Subject Classifications: 35A15, 35B33, 35J62.
Key Words: Multiple positive solutions; Schrodinger-Poisson system;
           critical Sobolev exponent; Nehari manifold; 
           Ljusternik-Schnirelmann category.