Multiple positive solutions for Schrodinger-Poisson systems involving concave-convex nonlinearities
Texas State University, Department of Mathematics
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.
Multiple positive solutions, Schrödinger-Poisson system, Critical Sobolev exponent, Nehari manifold, Ljusternik-Schnirelmann category
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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