Electron. J. Differential Equations, Vol. 2017 (2017), No. 268, pp. 1-18.

Multiple nodal solutions of nonlinear Choquard equations

Zhihua Huang, Jianfu Yang, Weilin Yu

Abstract:
In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation
$$\displaylines{ -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \quad \text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$
where $p\in (5/2,5)$. We show that for any positive integer k, the above problem has at least one radially symmetrical solution changing sign exactly k-times.

Submitted July 15, 2017. Published October 27, 2017.
Math Subject Classifications: 35J61, 35B33, 35B38, 35B65.
Key Words: Nonlinear Choquard equations; nodal solutions; nonlocal term.

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  Zhihua Huang
Department of Mathematics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: zhhuang2016@126.com
Jianfu Yang
Department of Mathematics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com
  Weilin Yu
Department of Mathematics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: williamyu2065@163.com

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