Least energy sign-changing solutions for the nonlinear Schrodinger-Poisson system
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Date
2017-11-13
Authors
Ji, Chao
Fang, Fei
Zhang, Binlin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence of the least energy sign-changing solutions for the Schrödinger-Poisson system
-∆u + V(x)u + λφ(x)u = ƒ(u), in ℝ3,
-∆φ = u2, in ℝ3
Because the so-called nonlocal term λφ(x)u is involved in the system, the variational functional of the above system has totally different properties from the case of λ = 0. By constraint variational method and quantitative deformation lemma, we prove that the above problem has one least energy sign-changing solution. Moreover, for any λ > 0, we show that the energy of a sign-changing solution is strictly larger than twice of the ground state energy. Finally, we consider λ as a parameter and study the convergence property of the least energy sign-changing solutions as λ ↘ 0.
Description
Keywords
Schrödinger-Poisson system, Sign-changing solutions, Constraint variational method, Quantitative deformation lemma
Citation
Ji, C., Fang, F., & Zhang, B. (2017). Least energy sign-changing solutions for the nonlinear Schrodinger-Poisson system. <i>Electronic Journal of Differential Equations, 2017</i>(282), pp. 1-13.