Multiple nodal solutions of nonlinear Choquard equations

• Main Authors: Zhihua Huang, Jianfu Yang, Weilin Yu
• Format: Article
• Language: English
• Published: Texas State University 2017-10-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlinear Choquard equations; nodal solutions; nonlocal term
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/268/abstr.html

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.