Least energy sign-changing solutions for the nonlinear Schrodinger-Poisson system
Texas State University, Department of Mathematics
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.
Schrödinger-Poisson system, Sign-changing solutions, Constraint variational method, Quantitative deformation lemma
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.