Multiple positive solutions for Schrodinger-Poisson systems involving concave-convex nonlinearities
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Date
2019-07-16
Authors
Fan, Haining
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the existence of multiple positive solutions for Schrödinger-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.
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Keywords
Multiple positive solutions, Schrödinger-Poisson system, Critical Sobolev exponent, Nehari manifold, Ljusternik-Schnirelmann category
Citation
Fan, H. (2019). Multiple positive solutions for Schrodinger-Poisson systems involving concave-convex nonlinearities. <i>Electronic Journal of Differential Equations, 2019</i>(86), pp. 1-19.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.