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.
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| Haining Fan |
School of Science
China University of Mining and Technology
Xuzhou 221116, China
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