Infinitely many sign-changing solutions for planar Schrödinger-Newton equations

Wenbo Wang, Quanqing Li, Yuanyang Yu and Yongkun Li ()
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Wenbo Wang: Yunnan University
Quanqing Li: Honghe University
Yuanyang Yu: CAS
Yongkun Li: Yunnan University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 149-161

Abstract: Abstract In this paper, we study the following planar Schrödinger-Newton system with a Coulomb potential $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+ W(x)u+ 2\pi \phi u+\int _{{\mathbb {R}}^{2}}\frac{[u(y)]^{2}}{|x-y|}dyu = f(u), &{} \text{in}\,{\mathbb {R}}^{2},\\ \Delta \phi =u^2, &{} \text{in}\,{\mathbb {R}}^{2}, \end{array}\right. \end{aligned}$$ - Δ u + W ( x ) u + 2 π ϕ u + ∫ R 2 [ u ( y ) ] 2 | x - y | d y u = f ( u ) , in R 2 , Δ ϕ = u 2 , in R 2 , where f is super-linear at zero and subcritical at infinity. We obtain infinitely many sign-changing solutions of the above problem via the invariant sets of descending flow.

Keywords: Sign-changing solutions; Invariant sets of descending flow; Perturbation; 35J50; 35J20; 35J10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00079-8

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