Multiple nodal solutions of nonlinear Choquard equations
Texas State University, Department of Mathematics
In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation -∆u + u = (|x|-1 ∗ |u|p)|u|p-2u in ℝ3, u ∈ H1 (ℝ3), where p ∈ (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.
Nonlinear Choquard equations, Nodal solutions, Nonlocal term
Huang, Z., Yang, J., & Yu, W. (2017). Multiple nodal solutions of nonlinear Choquard equations. <i>Electronic Journal of Differential Equations, 2017</i>(268), pp. 1-18.