School of Science
China University of Mining and Technology
Xuzhou 221116, China
email: fanhaining888@163.com
Haining Fan
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.
Show me the PDF file (361 KB), TEX file for this article.
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Haining Fan School of Science China University of Mining and Technology Xuzhou 221116, China email: fanhaining888@163.com |
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