Multiple nodal solutions of nonlinear Choquard equations

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.

Keywords

• Nonlinear Choquard equations
• nodal solutions
• nonlocal term